36 STAT Questions please help

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Use Excel to find the critical value of z for each hypothesis test. (Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.)      (a) 5 percent level of significance, two­tailed test.       

  Critical value of z ±           (b) 2 percent level of significance, right­tailed test.      

  Critical value of z         (c) 10 percent level of significance, left­tailed test.      

  Critical value of z   

References

Worksheet Difficulty: 1­Easy Learning Objective: 09­05 Find critical values of z or t in tables or by using Excel.

 

[The following information applies to the questions displayed below.]   GreenBeam Ltd. claims that its compact fluorescent bulbs average no more than 3.4 mg of mercury. A sample of 40 bulbs shows a mean of 3.46 mg of mercury.

(a) State the hypotheses for a right-tailed test, using GreenBeam’s claim as the null hypothesis about the mean.

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Hint #1

References

Multiple Choice Learning Objective: 09-04 Formulate a null and alternative hypothesis for μ or π.

Learning Objective: 09-06 Perform a hypothesis test for a mean with known σ using z.

Difficulty: 2- Medium

Learning Objective: 09-05 Find critical values of z or t in tables or by using Excel.

Learning Objective: 09-08 Use tables or Excel to find the p-value in tests of μ.

(b)Assuming a known standard deviation of 0.2 mg, calculate the z test statistic to test the manufacturer's claim. (Round your answer to 2 decimal places.)

       Test statistic   

Hint #1

References

Worksheet Learning Objective: 09­04 Formulate a null and alternative hypothesis for μ or π.

Learning Objective: 09­06 Perform a hypothesis test for a mean with known σ using z.

Difficulty: 2­ Medium

Learning Objective: 09­05 Find critical values of z or t in tables or by using Excel.

Learning Objective: 09­08 Use tables or Excel to find the p­value in tests of μ.

 

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(c) At the 5 percent level of significance (α = 0.05) does the sample exceed the manufacturer’s claim?    

  No Yes

Hint #1

References

Worksheet Learning Objective: 09­04 Formulate a null and alternative hypothesis for μ or π.

Learning Objective: 09­06 Perform a hypothesis test for a mean with known σ using z.

Difficulty: 2­ Medium

Learning Objective: 09­05 Find critical values of z or t in tables or by using Excel.

Learning Objective: 09­08 Use tables or Excel to find the p­value in tests of μ.

 

(d) Find the p­value. (Round your answer to 4 decimal places.)    

  p­value   

Hint #1

References

Worksheet Learning Objective: 09­04 Formulate a null and alternative hypothesis for μ or π.

Learning Objective: 09­06 Perform a hypothesis test for a mean with known σ using z.

Difficulty: 2­ Medium

Learning Objective: 09­05 Find critical values of z or t in tables or by using Excel.

Learning Objective: 09­08 Use tables or Excel to find the p­value in tests of μ.

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Using Appendix C­1 or Appendix C­2 find the p­value for each test statistic. (Round your answers to 4 decimal places.)     

    Test

Statistic p­value (a) Right­tailed test z = +2.74    (b) Left­tailed test z = ­2.63    (c) Two­tailed test z = ­2.04   

References

Worksheet Difficulty: 2­Medium Learning Objective: 09­08 Use tables or Excel to find the p­value in tests of μ.

 

 [The following information applies to the questions displayed below.]

The mean arrival rate of flights at O'Hare Airport in marginal weather is 195 flights per hour with a historical standard deviation of 14 flights. To increase arrivals, a new air traffic control procedure is implemented. In the next 30 days of marginal weather, the mean arrival rate is 205 flights per hour.

                    214 235 214 193 212 199 216 189 184 204 217 194 188 188 210 187 185 229 213 206 197 203 207 192 213 200 234 205 224 198

 Click here for the Excel Data File

(a) Set up a right-tailed decision rule at α = 0.025 to decide whether there has been a significant increase in the mean number of arrivals per hour. Choose the appropriate hypothesis.

H1: μ < 195, reject H1 if z > 1.960

H1: μ > 195, reject H1 if z < 1.960

H0: μ ≤ 195, reject H0 if z > 1.960

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H0: μ ≥ 195, reject H0 if z < 1.960

References

Multiple Choice Learning Objective: 09-05 Find critical values of z or t in tables or by using Excel.

Learning Objective: 09-08 Use tables or Excel to find the p-value in tests of μ.

Difficulty: 3-Hard Learning Objective: 09-06 Perform a hypothesis test for a mean with known σ using z.

(b­1) Calculate the test statistic. (Round your answer to 2 decimal places.)

  Test statistic   

References

Worksheet Learning Objective: 09­05 Find critical values of z or t in tables or by using Excel.

Learning Objective: 09­08 Use tables or Excel to find the p­value in tests of μ.

Difficulty: 3­ Hard

Learning Objective: 09­06 Perform a hypothesis test for a mean with known σ using z.

 

(b-2) What is the conclusion?

There has not been a significant increase in the average number of flight departures.

There has been a significant increase in the average number of flight departures.

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References

Multiple Choice Learning Objective: 09-05 Find critical values of z or t in tables or by using Excel.

Learning Objective: 09-08 Use tables or Excel to find the p-value in tests of μ.

Difficulty: 3-Hard Learning Objective: 09-06 Perform a hypothesis test for a mean with known σ using z.

(b-3) Would the decision have been different if you used α = 0.01?

Yes

No

References

Multiple Choice Learning Objective: 09-05 Find critical values of z or t in tables or by using Excel.

Learning Objective: 09-08 Use tables or Excel to find the p-value in tests of μ.

Difficulty: 3-Hard Learning Objective: 09-06 Perform a hypothesis test for a mean with known σ using z.

(c)  What assumptions are you making, if any? rev: 10_13_2012

We have assumed that the data follow a uniform distribution.

We have assumed that the type of distribution does not matter.

We have assumed a normal population or at least one that is not badly skewed.

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References

Multiple Choice Learning Objective: 09-05 Find critical values of z or t in tables or by using Excel.

Learning Objective: 09-08 Use tables or Excel to find the p-value in tests of μ.

Difficulty: 3-Hard Learning Objective: 09-06 Perform a hypothesis test for a mean with known σ using z.

[The following information applies to the questions displayed below.]

The Scottsdale fire department aims to respond to fire calls in 6 minutes or less, on average. Response times are normally distributed with a standard deviation of 1.3 minute. Would a sample of 18 fire calls with a mean response time of 6 minutes 20 seconds provide sufficient evidence to show that the goal is not being met at α = 0.01?

(a) Choose the appropriate hypotheses.

H0: µ ≥ 6 minutes; H1: µ < 6 minutes, Reject H0 if zcalc > 2.326

H0: µ ≤ 6 minutes; H1: µ > 6 minutes, Reject H0 if zcalc > 2.326

References

Multiple Choice Learning Objective: 09-04 Formulate a null and alternative hypothesis for μ or π.

Learning Objective: 09-06 Perform a hypothesis test for a mean with known σ using z.

Difficulty: 2- Medium

Learning Objective: 09-05 Find critical values of z or t in tables or by using Excel.

Learning Objective: 09-08 Use tables or Excel to find the p-value in tests of μ.

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(b)Calculate the value of Test statistic. (Carry out all intermediate calculations to at least four decimal places. Round your answer to 3 decimal places.)

  zcalc   

References

Worksheet Learning Objective: 09­04 Formulate a null and alternative hypothesis for μ or π.

Learning Objective: 09­06 Perform a hypothesis test for a mean with known σ using z.

Difficulty: 2­ Medium

Learning Objective: 09­05 Find critical values of z or t in tables or by using Excel.

Learning Objective: 09­08 Use tables or Excel to find the p­value in tests of μ.

 

(c) Use Excel to find the p­value. (Round your answer to 4 decimal places.)

  p­value   

References

Worksheet Learning Objective: 09­04 Formulate a null and alternative hypothesis for μ or π.

Learning Objective: 09­06 Perform a hypothesis test for a mean with known σ using z.

Difficulty: 2­ Medium

Learning Objective: 09­05 Find critical values of z or t in tables or by using Excel.

Learning Objective: 09­08 Use tables or Excel to find the p­value in tests of μ.

 

(d) If α =0.01, we would have

Fail to reject the null hypothesis.

Reject the null hypothesis.

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References

Multiple Choice Learning Objective: 09-04 Formulate a null and alternative hypothesis for μ or π.

Learning Objective: 09-06 Perform a hypothesis test for a mean with known σ using z.

Difficulty: 2- Medium

Learning Objective: 09-05 Find critical values of z or t in tables or by using Excel.

Learning Objective: 09-08 Use tables or Excel to find the p-value in tests of μ.

The lifespan of xenon metal halide arc­discharge bulbs for aircraft landing lights is normally distributed with a mean of 2,800 hours and a standard deviation of 390 hours.

(a) If a new ballast system shows a mean life of 3,040 hours in a test on a sample of 8 prototype new bulbs, would you conclude that the new lamp’s mean life exceeds the current mean life at α = 0.01?

    

  Yes No

(b)What is the p­value? (Round your answers to 4 decimal places.)

  p­value   

References

Worksheet Learning Objective: 09­05 Find critical values of z or t in tables or by using Excel.

Difficulty: 1­ Easy

Learning Objective: 09­06 Perform a hypothesis test for a mean with known σ using z.

 

[The following information applies to the questions displayed below.]

The manufacturer of an airport baggage scanning machine claims it can handle an average of 588 bags per hour.

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 18. Award: 2.77 points    

(a-1) At α = 0.05 in a left-tailed test, would a sample of 16 randomly chosen hours with a mean of 564 and a standard deviation of 46 indicate that the manufacturer's claim is overstated? Choose the appropriate hypothesis.

H0: μ < 588. Reject H0 if tcalc > -1.753

H1: μ < 588. Reject H1 if tcalc > -1.753

H0: μ ≥ 588. Reject H0 if tcalc < -1.753

H1: μ ≥ 588. Reject H1 if tcalc < -1.753

References

Multiple Choice Learning Objective: 09-04 Formulate a null and alternative hypothesis for μ or π.

Learning Objective: 09-08 Use tables or Excel to find the p-value in tests of μ.

Difficulty: 2- Medium

Learning Objective: 09-07 Perform a hypothesis test for a mean with unknown σ using t.

(a­2) State the conclusion.    

  tcalc = ­2.087. There is significant evidence to reject the manufacturer’s claim. tcalc = ­2.087. There is not enough evidence to reject the manufacturer’s claim.

References

Multiple Choice Learning Objective: 09­04 Formulate a null and alternative hypothesis for μ or π.

Learning Objective: 09­08 Use tables or Excel to find the p­value in tests of μ.

Difficulty: 2­ Medium

Learning Objective: 09­07 Perform a hypothesis test for a mean with unknown σ using t.

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[The following information applies to the questions displayed below.]     The average weight of a package of rolled oats is supposed to be at least 16 ounces. A sample of 18 packages shows a mean of 15.81 ounces with a standard deviation of 0.48 ounce.

(a) At the 5 percent level of significance, is the true mean smaller than the specification? Clearly state your hypotheses and decision rule.

      H0: μ ≥ 16. Reject H0 if tcalc < ­1.740

H1: μ < 16. Reject H1 if tcalc < ­1.740 H1: μ < 16. Reject H1 if tcalc > ­1.740 H0: μ ≥ 18. Reject H0 if tcalc > ­1.740

References

Multiple Choice Learning Objective: 09­04 Formulate a null and alternative hypothesis for μ or π.

Learning Objective: 09­08 Use tables or Excel to find the p­value in tests of μ.

Difficulty: 2­ Medium

Learning Objective: 09­07 Perform a hypothesis test for a mean with unknown σ using t.

 

(b) If α = 0.01, we would have

failed to reject the null hypothesis.

rejected the null hypothesis.

References

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Multiple Choice Learning Objective: 09-04 Formulate a null and alternative hypothesis for μ or π.

Learning Objective: 09-08 Use tables or Excel to find the p-value in tests of μ.

Difficulty: 2- Medium

Learning Objective: 09-07 Perform a hypothesis test for a mean with unknown σ using t.

(c) Use Excel to find the p­value. (Round your answer to 4 decimal places.)

  p­value   

References

Worksheet Learning Objective: 09­04 Formulate a null and alternative hypothesis for μ or π.

Learning Objective: 09­08 Use tables or Excel to find the p­value in tests of μ.

Difficulty: 2­ Medium

Learning Objective: 09­07 Perform a hypothesis test for a mean with unknown σ using t.

 

 [The following information applies to the questions displayed below.]     The number of entrees purchased in a single order at a Noodles & Company restaurant has had an historical average of 1.55 entrees per order. On a particular Saturday afternoon, a random sample of 38 Noodles orders had a mean number of entrees equal to 1.65 with a standard deviation equal to 0.7. At the 2 percent level of significance, does this sample show that the average number of entrees per order was greater than expected?

(a) Choose the correct null and alternative hypotheses.

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H0:  ≤ 1.55 vs. H1:  > 1.55

H0:  = 1.55 vs. H1:  ≠ 1.55

H0:  ≥ 1.55 vs. H1:  < 1.55

Hint #1

References

Multiple Choice Learning Objective: 09-04 Formulate a null and alternative hypothesis for μ or π.

Difficulty: 2- Medium

Learning Objective: 09-07 Perform a hypothesis test for a mean with unknown σ using t.

(b­1) Calculate the t statistic. (Round your answer to 2 decimal places.)   

  tcalc   

Hint #1

References

Worksheet Learning Objective: 09­04 Formulate a null and alternative hypothesis for μ or π.

Difficulty: 2­ Medium

Learning Objective: 09­07 Perform a hypothesis test for a mean with unknown σ using t.

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(b­2) Find the p­value. (Round your answer to 4 decimal places.)   

  p­value   

Hint #1

References

Worksheet Learning Objective: 09­04 Formulate a null and alternative hypothesis for μ or π.

Difficulty: 2­ Medium

Learning Objective: 09­07 Perform a hypothesis test for a mean with unknown σ using t.

 

(c) Choose the correct conclusion.

Because the p-value is less than 0.02, conclude that there is evidence to indicate a significant increase in the average number of entrees per order.

Because the p-value is greater than 0.02, conclude that there is no evidence to indicate a significant increase in the average number of entrees per order.

Hint #1

References

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Multiple Choice Learning Objective: 09-04 Formulate a null and alternative hypothesis for μ or π.

Difficulty: 2- Medium

Learning Objective: 09-07 Perform a hypothesis test for a mean with unknown σ using t.

[The following information applies to the questions displayed below.]

  In 2008, a small dealership leased 21 Suburu Outbacks on 2-year leases. When the cars were returned in 2010, the mileage was recorded (see below).

               

 40,018 24,992 14,301 17,334 44,755 44,541 20,227  33,329 24,243 41,763 58,361 35,832 25,728 28,955  25,085 43,346 23,977 43,537 53,608 31,859 36,759

   Click here for the Excel Data File

rev: 04_06_2015_QC_CS-8527

(a) Is the dealer's mean significantly greater than the national average for 2-year leases is 29,643 miles. Using the 10 percent level of significance. Choose the appropriate hypothesis.

rev: 04_06_2015_QC_CS-8527

H0: μ > 29,643, reject H1 if tcalc > 1.325

H1: μ ≤ 29,643, reject H0 if tcalc > 1.325

H1: μ > 29,643, reject H1 if tcalc > 1.325

H0: μ ≤ 29,643, reject H0 if tcalc > 1.325

References

Multiple Choice Learning Objective: 09-04 Formulate a null and alternative hypothesis for μ or π.

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 28. Award: 2.77 points    

Difficulty: 2- Medium

Learning Objective: 09-07 Perform a hypothesis test for a mean with unknown σ using t.

(b)Calculate the test statistic. (Round your answer to 3 decimal places.)     

  Test statistic   

References

Worksheet Learning Objective: 09­04 Formulate a null and alternative hypothesis for μ or π.

Difficulty: 2­ Medium

Learning Objective: 09­07 Perform a hypothesis test for a mean with unknown σ using t.

 

(c) The dealer's cars show significantly greater mean number of miles than the national average at the 10% level.

No

Yes

References

Multiple Choice Learning Objective: 09-04 Formulate a null and alternative hypothesis for μ or π.

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Difficulty: 2- Medium

Learning Objective: 09-07 Perform a hypothesis test for a mean with unknown σ using t.

Calculate the test statistic and p­value for each sample. Use Appendix C­2 to calculate the p­value. (Negative values should be indicated by a minus sign. Round your test statistic to 3 decimal places and p­value to 4 decimal places.)

    Test Statistic p­value

  (a) H0: π ≤ 0.45 versus H1: π > 0.45, α = 0.05, x = 43, n = 82           (b) H0: π = 0.30 versus H1: π ≠ 0.30, α = 0.05, x = 17, n = 38           (c) H0: π ≥ 0.10 versus H1: π < 0.10, α = 0.01, x = 6, n = 103       

rev: 04_16_2014_QC_48525

Hint #1

References

Worksheet Difficulty: 2­Medium Learning Objective: 09­09 Perform a hypothesis test for a proportion and find the p­value.

 

[The following information applies to the questions displayed below.]

In a recent survey, 10 percent of the participants rated Pepsi as being "concerned with my health." PepsiCo's response included a new "Smart Spot" symbol on its products that meet certain nutrition criteria, to help consumers who seek more healthful eating options.

(a) Suppose a follow­up survey showing that 50 of 400 persons now rate Pepsi as being "concerned with my health", calculate the z statistic. (Round your answer to 3 decimal places.)

  zcalc   

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References

Worksheet Learning Objective: 09­04 Formulate a null and alternative hypothesis for μ or π.

Difficulty: 2­ Medium

Learning Objective: 09­09 Perform a hypothesis test for a proportion and find the p­value.

 

(b) At α = 0.05, would a follow-up survey showing that 50 of 400 persons now rate Pepsi as being "concerned with my health" provide sufficient evidence that the percentage has increased?

Yes

No

References

Multiple Choice Learning Objective: 09-04 Formulate a null and alternative hypothesis for μ or π.

Difficulty: 2- Medium

Learning Objective: 09-09 Perform a hypothesis test for a proportion and find the p-value.

To combat antibiotic resistance, the Quality Improvement Consortium recommends a throat swab to confirm strep throat before a physician prescribes antibiotics to children under age 5. In a random sample of 61 children who received antibiotics for throat infections, 14 did not have a throat swab. At α = 0.05, is this a statistically significant reduction over last year’s national rate of 40 percent.

(a­1) Choose the correct null and alternative hypotheses.    

 

H0: π ≤ 0.40 vs. H1: π > 0.40 H0: π ≥ 0.40 vs. H1: π < 0.40

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H0: π = 0.40 vs. H1: π ≠ 0.40

(a­2) Calculate  the  critical  value.  (Negative  value  should  indicated  by  a  minus  sign.  Round  your answer to 3 decimal places.)

        Critical value     

      (a­3) Calculate  the  Test  statistic.  (Negative  value  should  indicated  by  a  minus  sign.  Round  your

answer to 2 decimal places.)       

  Test statistic            (a­4) Interpret the results.    

  reject H0 fail to reject H0

(b) Is it safe to assume normality of the sample proportion p?    

  No, normality is not justified. Yes, normality is justified.

References

Worksheet Learning Objective: 09­04 Formulate a null and alternative hypothesis for μ or π.

Difficulty: 2­ Medium

Learning Objective: 09­09 Perform a hypothesis test for a proportion and find the p­value.

 

A coin was flipped 15 times and came up heads 11 times.   (a) The assumption of normality is justified.    

  Yes No

  (b­1) Calculate a p­value for the observed sample outcome, using the normal distribution. (Round your z­

value to two decimal places. Round your answer to 4 decimal places.)

  p­value   

(b­2) At the 0.05 level of significance in a right­tailed test, is the coin biased toward heads?    

  No Yes

11/19/2015 Assignment Print View

http://ezto.mheducation.com/hm.tpx 20/21

 34. Award: 2.77 points    

(c) Use Excel to calculate the binomial probability P(X ≥ 11 | n = 15, π = 0.50) = 1 − P(X ≤ 10 | n = 15, π = 0.50). (Round your answer to 4 decimal places.)

  P(X ≥ 11)   

(d) The normal probability is    

  An approximation The same as the binomial probability

References

Worksheet Learning Objective: 09­04 Formulate a null and alternative hypothesis for μ or π.

Difficulty: 3­ Hard

Learning Objective: 09­09 Perform a hypothesis test for a proportion and find the p­value.

 

[The following information applies to the questions displayed below.]    Perfect pitch is the ability to identify musical notes correctly without hearing another note as a reference. The probability that a randomly chosen person has perfect pitch is 0.0005.

(a) If 42 students at Julliard School of Music are tested, and 3 are found to have perfect pitch, would you conclude at the 0.01 level of significance that Julliard students are more likely than the general population to have perfect pitch?

Yes

No

References

Multiple Choice Learning Objective: 09-04 Formulate a null and alternative hypothesis for μ or π.

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11/19/2015 Assignment Print View

http://ezto.mheducation.com/hm.tpx 21/21

 35. Award: 2.77 points    

 36. Award: 3.05 points    

Difficulty: 3-Hard Learning Objective: 09-09 Perform a hypothesis test for a proportion and find the p-value.

(b) Normality should not be assumed because

the product of n and π0 is too small.

all students had perfect pitch.

only 3 students had perfect pitch.

no student had perfect pitch.

References

Multiple Choice Learning Objective: 09-04 Formulate a null and alternative hypothesis for μ or π.

Difficulty: 3-Hard Learning Objective: 09-09 Perform a hypothesis test for a proportion and find the p-value.

This question and its points have been dropped for all students

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