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# Hypothesis Testing and Statistical Analysis of Scenarios

1. The owner of the Kate and Edith Cake Company state that the average number of buns sold daily was 1,500. A worker in the store wants to test the accuracy of the boss's statement. A random sample of 36 days showed that the average daily sales were 1,450 buns. Using a level of significance of .01 and assuming that the standard deviation is 120, what should the worker conclude?

2. Mr. Tyrone Hops, the supervisor of the local brewery, wants to make sure that the average volume of the Super-Duper cans is 16 ounces. If the average volume is significantly less than 16 ounces, customers (and various agencies) would likely complain, prompting undesirable publicity. The physical size of the can does not allow an average volume significantly above 16 ounces. A random sample of 36 cans showed a sample mean of 15.7 ounces. Assuming that the standard deviation is 0.2 ounces, conduct a hypothesis test with the level of significance equal to .01.

3. Dr. I. M Sain, a psychologist, administered IQ tests to determine if female college students were as smart as male students. The sample of 40 females had a mean score of 131 with a standard deviation of 15. The sample of 36 males had a mean of 126 and a standard deviation of 17. At the .01 level of significance, is there a difference?

4. Discount Stores Corporation owns outlet A and outlet B. For the past year, outlet A has spent more dollars on advertising widgets than outlet B. The corporation wants to determine if the advertising has resulted in more sales for outlet A. A sample of 36 days at outlet A had a mean of 170 widgets sold daily. A sample of 36 days at outlet B had a mean of 165. Assuming that the variance of the first test is 36 and the variance of the second test is 25 respectfully, what would be concluded if a test were conducted at the .05 level of significance?

5. The following table reports the earnings per share (in dollars) for the Heban Lumber Mill from 1997 to 2003.

Year 1997 1998 1999 2000 2001 2002 2003
Earnings per share 1.56 1.86 2.17 2.41 2.67 2.97 3.40

a. Plot the data on a chart.
b. Estimate the linear trend equation by drawing a line through the data.
c. Determine the least squares trend equation.
d. Estimate the earnings per share for 2004.

6. A major oil company is studying the relationship between the daily traffic count and the number of gallons of gasoline pumped at company stations. A sample of eight company owned stations is selected and the following information obtained:

Location Total Gallons of Gas Pumped (000) Traffic Count of Vehicles (000)
West St. 120 4
Willouhby St. 180 6
Mallard Rd. 140 5
Pheasant Rd. 150 5
I-75 210 8
Kinzua Rd. 100 3
Front St. 90 3
Indiana Ave. 80 2

a. Develop a scatter diagram with the amount of gasoline pumped as the dependent variable.
b. Compute the coefficient of correlation
c. Compute the coefficient of determination.
d. Interpret the meaning of the coefficient of determination.
e. Test to determine whether the correlation in the population is zero, versus the alternate hypothesis that the correlation is greater than zero. Use the 0.05 significance level.

#### Solution Summary

This solution explores hypothesis and statistical analysis of scenarios with step-by-step calculations and explanations. It provides the null and alternative hypothesis and tests the calculated test statistic against the critical value to either accept or reject the null hypothesis. It also includes graphs, linear trend equations, and coefficient of determination and correlation calculations.

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