Question 1

CNNBC recently reported that the mean annual cost of auto insurance is 1036 dollars. Assume the standard deviation is 228 dollars. You take a simple random sample of 89 auto insurance policies. Find the probability that a single randomly selected value is less than 995 dollars. P(X< 995) = Find the probability that a sample of sizen=89n=89is randomly selected with a mean less than 995 dollars. P(M< 995) = Enter the answers as numbers accurate to 4 decimal places.

Question 2

If n=580 and p' (p-prime) = 0.28, construct a 90% confidence interval. Give the answers to three decimals. < p < Question 3

In a survey, 28 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $32 and standard deviation of $4. Construct a confidence interval at a 95% confidence level. Give the answers to one decimal place. Question 4

SAT scores are distributed with a mean of 1,500 and a standard deviation of 300. You are interested in estimating the average SAT score of first year students at your college. If you would like to limit the margin of error of your 95% confidence interval to 25 points, how many students should you sample?

Question 5

Explain how a court trial is like hypothesis testing. Include the steps of a hypothesis test and why a verdict is "not guilty" instead of innocent.

Question 6

You measure 44 textbooks' weights, and find they have a mean weight of 61 ounces. Assume the population standard deviation is 13 ounces. Based on this, construct a 90% confidence interval for the true population mean textbook weight. Give the answers as decimals, to two places Question 7

Food inspectors inspect samples of food products to see if they are safe. This can be thought of as a hypothesis test with the following hypotheses.

H₀: the food is safe

H_a: the food is not safe

The following is an example of what type of error?

The sample suggests that the food is safe, but it actually is not safe.

• type I
• type II
• not an error

Question 8

Test the claim that the mean GPA of night students is significantly different than 2 at the 0.1 significance level. The null and alternative hypothesis would be:

H0:=2H0:=2 H1:2H1:2 H0:p0.5H0:p0.5 H1:p<0.5H1:p<0.5 H0:2H0:2 H1:>2H1:>2 H0:p=0.5H0:p=0.5 H1:p0.5H1:p0.5 H0:p0.5H0:p0.5 H1:p>0.5H1:p>0.5 H0:2H0:2 H1:<2H1:<2 The test is:

left-tailed right-tailed two-tailed Based on a sample of 75 people, the sample mean GPA was 1.99 with a standard deviation of 0.04 The p-value is: (to 2 decimals) Based on this we:

• Fail to reject the null hypothesis
• Reject the null hypothesis

Question 9

Test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the .025 significance level. The null and alternative hypothesis would be:

H0:M=FH0:M=F H1:MFH1:MF H0:pM=pFH0:pM=pF H1:pM>pFH1:pM>pF H0:pM=pFH0:pM=pF H1:pMFH1:M>F H0:M=FH0:M=F H1:M

• Fail to reject the null hypothesis
• Reject the null hypothesis

Question 10

Test the claim that the mean GPA of night students is larger than the mean GPA of day students at the 0.005 significance level. The null and alternative hypothesis would be:

H0:NDH0:ND H1:N>DH1:N>D H0:pN=pDH0:pN=pD H1:pNpDH1:pNpD H0:N=DH0:N=D H1:NDH1:ND H0:NDH0:ND H1:NpDH1:pN>pD The test is:

two-tailed left-tailed right-tailed The sample consisted of 35 night students, with a sample mean GPA of 2.5 and a standard deviation of 0.02, and 35 day students, with a sample mean GPA of 2.45 and a standard deviation of 0.04. The test statistic is: (to 2 decimals) The p-value is: (to 2 decimals) Based on this we:

• Reject the null hypothesis
• Fail to reject the null hypothesis

Question 11

For each scenario listed on the left, determine whether the scenario represents an Indepenent Samples or Matched pairs situation by placing the appropriate letter in the box provided.

• -ab Comparing pain levels before and after treatment with magnetic therapy
• -ab Comparing the number of speeding tickets received by men to the number received by women
• -ab Comparing pre-test scores before training to post-test scores
• -ab Comparing pain levels of a group receiving a placebo to a group receiving a medicine

1. Independent Samples
2. Matched Pairs

Question 12

What does "degrees of freedom" measure?

Question 13

In the discussion of Nissan's Leaf, we looked at two hypothesis tests for the same 6 measurements of the range. The first treated Nissan's claim as something to prove and found the claim was not proved with this data. The second test gave Nissan the benefit of the doubt and found we would not reject their claim based on this data. The conclusions appear contradictory. This chart illustrates assuming the population mean is 74 or 77 miles.

As a statistician,explain this to your client using a court trial as a parallel.