# Test of hypotheses.

1. The wages for middle managers in a certain industry are thought to be no more than $45,000.00. A wage survey of 30 managers has a mean income of $46,260.00. Test the hypothesis at a 1% significance level. Does it appear that the average annual income is greater than $45,000.00? The population standard deviation is assumed to be $5,200.00.

2. Determine the P-value for a two-tailed test when z = -0.17.

3. A credit card issuer claims that the average annual expenditure on accounts is $1123.00. A sample of 15 accounts showed a mean of $1344.00 and a standard deviation of $231.00. Do the sample data indicate that the annual average is higher? Test the claim at a 5% significance level.

4. A car service operates in two towns. The company manager wants to determine whether there is a difference in the gasoline consumption between the two towns. Gasoline consumption was studied. The attached summary provides the statistics for the two towns.

At a 5% significance level, do the data indicate that the gasoline consumption is greater in town 1 than in town 2? Assume the criteria for using pooled t-test are satisfied.

5. Six individuals took a pill to lose weight. Their weights before and after the program were recorded. The statistics are summarized in the attachment.

At a 10% significance level, can we conclude the pill is effective in reducing weight?

6. A certain additive is used in the preparation of a snack food product. In a sample of 1500 snack food eaters, 114 individuals were found to be allergic to the additive. Determine the 95% confidence interval for the proportion of snack food eaters, p, who are allergic to the additive.

7. Determine the sample size required to estimate the population proportion and satisfy the following criteria: a 95% confidence level, p= 0.49, and a margin of error of 0.01.

8. An athletic director believes that when a new sports program is introduced, the participation will be as shown in the attachment (the actual participation is also shown):

anticipated.

anticipated participation distribution

Category Percent

Freshman 10

Sophomore 20

Junior 40

Senior 30

Participation distribution observed

Category observed

Freshman 12

Sophomore 18

Junior 45

Senior 25

Test the hypothesis at a 10% significance level that the participation in the program is that which the athletic director anticipated.

9. A linear regression equation has a y-intercept equal to 400 and a slope of -7.5. Write the equation.

10. Given the attached statistics:

Sigma x = 55.9, Sigma y = 832.5, Sigma xy = 4376.95, Sigma x^2 = 365.05, n = 10, SST = 1532.865, SSR = 1456.690, SSE = 76.175

a. Find the regression equation.

b. Compute the coefficient of determination.

c. Compute the correlation coefficient.

d. Comment on the usefulness of the regression to make predictions.

11. Perform the correlation test {see attachment}

H0: correlation = 0

Ha: correlation < 0

At the 1% significance level, given n = 10 and r = -0.975.

12. Given the attached statistics, determine the 90% confidence interval for b1.

b1 = 17.903

n = 10

Sigma x = 41

Sigma x^2 = 199

#### Solution Summary

Answers questions on Test of hypothesis, p value, confidence interval, linear regression etc.