assist mat stat 3

Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible. If the answer is in %, show two decimal places.

Answer the following problems showing your work and explaining (or analyzing) your results. Submit your work in a typed Microsoft Word document.

1. The average score of a statistics class was 71 with a standard deviation of 10.

a. What is the z score of a student with a grade of 68? (2.5 pts)

b. What is the z score of a student with a grade of 80? (2.5 pts)

2. Using the same data in #1 answer the following:

a. Approximately 68% (one standard deviation) of the scores are between ________ and _________ (2.5 pts)

b. Approximately 95% (two standard deviation) of the scores are between _________ and _________ (2.5 pts)

3. Most values of a standard normal distribution are between __________. (3 pts)

a. -3 and 3

b. 0 and 1

c. 0 and 3

d. 1 and 3

4. (a) If the standard deviation of a data set is 1.3, what is the variance? (2.5 pts) (b) If the variance is 36, what is the standard deviation? (2.5 pts)

5. Let X have a normal distribution with mean µ = 20 and standard deviation σ = 4.  Determine the area in the normal curve for which:

a. P(X > 28) (2.5 pts)

b. P(X < 12) (2.5 pts)

c. P(16 < X < 24) (2.5 pts)

6. The IQ scores of students listed below are from a SAMPLE of MATH 300 class.

IQ Scores	92	110	105	96	120	100	90	98	110	95
	102	99	93	119	106	103	91	101	97	105

a. What is the mean IQ score? Round to the nearest whole number. (2.5 pts)

b. Compute the IQ scores within plus/minus one standard deviation? Two answers. Round to the nearest whole numbers. (2.5 pts)

c. Compute the IQ scores within plus/minus two standard deviation? Two answers. (2.5 pts)

7. Let X have a normal distribution with µ= 10 and standard deviation σ= 2. Transform X to the standard normal form Z and match the following probability statements: a) P(X>14)                                          1) P(Z<-1) b) P(X<8)                                            2) P(-2 < Z < 2) c) P(6 < X < 14)                                  3) P(Z > 2) a) is matched to ___________ (2.5 pts) b) is matched to ___________ (2.5 pts) c) is matched to ___________ (2.5 pts)

8. Let X have a normal distribution with mean µ= 30 and standard deviation σ= 10. Calculate P(X>40). Round to two decimal places. (4 pts)

9. For a standard normal variable Z, compute P(Z<1.5). Round your answer to two decimal places. (3 pts)

10. A larger standard deviation of a normal distribution indicates that the distribution becomes (2.5 pts)

a. narrower and more peaked

b. flatter and wider

c. more skewed to the right

d. more skewed to the left

1. A restaurant leaves a fishbowl on the counter for diners to drop their business cards. Once a month, a business card is pulled out to award one lucky diner with a free meal. Identify which type of sampling is used and why. (2 pts)

2. A test of the effectiveness of a new curriculum could begin by dividing an area by school district, then choosing a school or set number of schools at random and collecting data about all students in each. Identify which type of sampling is used and why. (2.5 pts)

3. A survey about timekeeping might divide the population by time zone, then take 100 random samples per zone. Identify which type of sampling is used and why. (2.5 pts)

4. A local TV station conducts an “Instant Poll” to predict the winner in the upcoming mayoral election. Evening news viewers were invited to phone in their votes, with the results to be announced on the late-night news. Based on the phone calls, the station predicted that Joseph Serra would win the election with 52% of the vote. They were wrong: Serra lost, getting only 46% of the vote. This faulty prediction may be the consequence of what kind of bias? (2.5 pts)

5. According to Abyss Consulting, the average age of viewers of “America’s Got Talent” is 25 years old. However, the producer of the show thinks it is higher than 25.

a. Write the null hypothesis Ho and alternative hypothesis Ha. (2.5 pts)

b. Is this a right-tailed, left-tailed, or two-tailed test? (2 pts)

6. A research analyst believes that average back-to-school spending is less than a trade group’s prediction of $606.

a. Write the null hypothesis Ho and alternative hypothesis Ha. (2.5 pts)\

b. Is this a right-tailed, left-tailed, or two-tailed test? (2 pts)\

7. A study found that, in 2005, 12.5% of workers belonged to unions. Suppose a sample of 400 workers is collected in 2006 to determine whether union efforts to organize have increased union membership. The sample result show that 68 of the workers belonged to unions. State the null hypothesis Ho and alternative hypothesis Ha. (2.5 pts)

8. Consider the null hypothesis Ho: The man is innocent of crime. Ha: The man is guilty of crime.

a. What is the Type I error? (2.5 pts)

b. What is the Type II error? (2.5 pts)

9. Using a random sample of n = 36, the sample mean is x ̅ = 2.92. Suppose that the population standard deviation is σ=0.18. Is the above statistical evidence sufficient to make the following claim: μ<3 at the 5% level of significance?

a. Write the null hypothesis Ho and alternative hypothesis Ha. (2.5 pts)

b. Calculate the standard error. (2.5 pts)

c. Calculate the z score. (2.5 pts)

d. Calculate the p value. (2.5 pts)

e. What is the conclusion? (2 pts)

10. Using a random sample of n = 50, the sample mean is x ̅ = 297.6. Suppose that the population standard deviation is σ=12. Is the above statistical evidence sufficient to make the following claim: μ>295 right tail, one tail at the 1% level of significance?

a. Write the null hypothesis Ho and alternative hypothesis Ha. (2.5 pts)

b. Calculate the standard error. (2.5 pts)

c. Calculate the z score. (2.5 pts)

d. Calculate the p value. (2.5 pts)

e. What is the conclusion? (2 pts)