Elementary Statistics Final

MATH 160 Ch 7 – 10 Practice Form B

Name________________ Assume that all samples have been randomly selected from a population with a normal distribution. 1) You randomly select and weigh 25 samples of an allergy medicine. The sample

standard deviation is 1.20 milligrams. Assuming the weights are normally distributed, construct a 99% confidence interval for σ, the population standard deviation. ( Round your answer to 3 decimal places.)

2) Nielsen Media Research wants to estimate the mean amount of time that full-time

college students spend watching television each weekday. FIND THE SAMPLE SIZE necessary to estimate the mean with a 17 minute margin of error. Assuming that a 95 % confidence level is desired. Also assume that a pilot study showed that

σ = 112.2 minutes.

TRUE / FALSE QUESTIONS: (circle the correct answer) 3) The Chi – square distribution is not a symmetric distribution: T / F

4) A correlation coefficient of 1 indicates that there is a strong positive linear

relationship. T / F

5) When predicting a value of y based on some given value of x, if no significant linear

correlation exists the best predicted y –value is found by substituting the x-value into

the regression equation. T / F

6) When doing a hypothesis test, the claim always goes in to the alternate hypothesis

(H_1) T / F

7) A standard deviation measures variability and is useful to know in determining

product reliability. T / F

8) When the p-value is greater than the significance level (alpha) we reject the H_0 (the

null hypothesis) T / F

You want to buy a vacuum cleaner, and a salesperson tells you the repair costs for the Eureka Whirlwind vacuum and the Hoover - Wind Tunnel vacuum are equal. You research the repair costs of 34 Eureka Whirlwinds and 46 Hoover Wind Tunnels. The results are listed below. Eureka Whirlwind Vacuum:

n1 = 34, x1 =50, s1 =10

Hoover – Wind Tunnel vacuum:

n2 = 46, x2 = 60, s2 =18

9) Construct a 99% confidence interval estimate of the difference between the two

population means. 10) Was the salesperson being truthful? Does there appear to be a difference between the

two vacuum cleaners? Explain.

A trial study on an experimental nasal spray vaccine for children produced the following results: 14 out of 1070 children who received the vaccine developed the flu while 95 out of the 532 children who did not use the experimental nasal spray developed the flu. Test the claim that the proportion of children who developed the flu was lower for those using the experimental nasal spray than for those children who did not use it. Use a significance level of .05 11) Where does the claim go? In the H_0 or in the H_1 ? 12) The null hypothesis is _____________ 13) The alternate hypothesis is ______________ 14) The test statistic is _______________ 15) The critical value is _______________ 16) The p-value is ______________ 17) Choose one. a) FAIL TO REJECT 0H b) REJECT 0H . 18) Is there sufficient sample evidence to support the stated claim. ? YES / NO

The Currier Aviation Company uses a new production method to manufacture aircraft altimeters. A simple random sample of 28 altimeters are tested in a pressure chamber. The sample has a standard deviation of 58.4 ft. At the 0.10 significance level, test the claim that the new production method manufactures altimeters with less variation than the old production method. (The old production method manufactures altimeters with a standard deviation of 43.7 ft) 19) Which parameter is being tested here? a) µ b) σ c) Ρ 20) What is the claim? _________ 21) The null hypothesis is _____________ 22) The alternate hypothesis is ______________ 23) The test statistic is

a) 15.118 b) 48.2199 c) 50.0059 d) 43.7 e) none of the above

24) The critical value is

a) 36.741 b) 37.916 c) 18.939 d) 18.114 e) none of the above

25) Which is the correct conclusion for the problem. _________ a) The sample data support the claim that the new production method manufactures altimeters

with less variation than the old production method b) There is not sufficient sample evidence to support the claim that the new production method

manufactures altimeters with less variation than the old production method c) There is sufficient evidence to warrant rejection of the claim that the new production method

manufactures altimeters with less variation than the old production method d) There is not sufficient evidence to warrant rejection of the claim that the new production method

manufactures altimeters with less variation than the old production method . 26) Based on the your results should Currier Aviation adopt this new production

method to manufacture altimeters is it really better than the old production method?

The following table shows the SAT scores for six students before and after an intensive tutoring session. Test the claim that the intensive tutoring session was effective in helping students raise their SAT scores. (Use a significance level of 0.05) Before 445 510 429 452 629 500 After 446 571 517 400 610 540 27) What is the claim? _________ 28) The null hypothesis is _____________ 29) The alternate hypothesis is ______________ 30) The test statistic is _______________ 31) The critical value is _______________ 32) The p-value is ______________ 33) Choose one. a) FAIL TO REJECT 0H b) REJECT 0H . 34) Is this intensive tutoring session effective in helping students raise their SAT scores. ? Explain – this is not just a YES / NO question.

35) Coffee sales and temperatures: The paired data below consists of outdoor temperature and coffee sales for a coffee shop for 6 randomly selected days. Temperature was recorded in Fahrenheit and coffee sales are in hundreds of dollars.

X Temperature ( F) 29 41 51 60 78 81 Y Coffee Sales ($) 26.2 24.8 19.7 20 11.4 11.2

TAKE ANSWERS TO 3 DECIMAL PLACES a) Find the value of the linear correlation coefficient (r) b) Is there a significant linear correlation? ( This is not just a “yes” or “no” question,

show all steps in a hypothesis test leading to your answer) c) If a significant linear correlation exists, find the regression equation. If there is no

significant linear correlation, find y . d) Find the best predicted coffee sales when the temperature reaches 70 degrees

Fahrenheit.

Assume that a simple random sample has been selected from a normally distributed population. Use a significance level of 0.01 to test the claim that the mean lifetime of Honda car engines is greater than 220,000 miles. The mean lifetime of a sample of 25 car engines is 226,450 miles and it is known that σ = 11,000 miles. 36) What is the null hypothesis? ____________ 37) What is the alternate hypothesis?____________ 38) Find the test statistic 39) The critical value is

40) The p-value is

41) Which is the correct conclusion for the problem. _________ a) The sample data support the claim that the mean lifetime of Honda car engines is greater

than 220,000 miles b) There is not sufficient sample evidence to support the claim that the mean lifetime of Honda

car engines is greater than 220,000 miles c) There is sufficient evidence to warrant rejection of the claim that the mean lifetime of Honda

car engines is greater than 220,000 miles d) There is not sufficient evidence to warrant rejection of the claim that the mean lifetime of

Honda car engines is greater than 220,000 miles.