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1. A dean of a business school is interested in determining whether the mean grade point...

1. A dean of a business school is interested in determining whether the mean grade point average (GPA) of students is less than 3.04. The population standard deviation is 0.41 A random sample of 200 students indicates a sample mean GPA of 2.94. A test is conducted at the 0.05 level of significance to determine whether the mean grade point average (GPA) of students is less than 3.04. What are the most appropriate null and alternative hypotheses for this test?

A. H0: µ ≤ 3.04   versus   H1: µ > 3.04

B. H0: µ ≥ 3.04   versus   H1: µ < 3.04

C. H0: µ = 3.04   versus   H1: µ ≠ 3.04

D. H0: µ < 3.04   versus   H1: µ ≥ 3.04

2. After interviewing a sample of 100 residents of New Taipei City, you find that the mean AGE of the sample respondents is 35 years with a standard deviation of 5.0, and that AGE seems fairly normally distributed. However, you are told that the average age of New Taipei City is less than 37 years ten years ago. Based on your sample data, you need to test whether the true average age of all New Taipei City residents is still less than 37 years now. At α = 0.05, calculate the test statistic and determine the statistical decision.

A. tSTAT = +4 and do not reject H0.

B. tSTAT = +4 and reject H0.

C. tSTAT = –4 and do not reject H0.

D. tSTAT = –4 and reject H0.

3.A report announced that the mean sales price of all new houses sold one year was $272,000. Assume that the population standard deviation of the prices is $100,000. If you select a random sample of 100 new houses, there is 70% chance that the sample mean sales price is higher than how much?

A. $266,750

B. $282,400

C. $277,250

D. $261,600

4. A prospective developer of a shopping mall in an area believes that the average annual income per capita in the area is $280,000. Historical data suggest that for the type of area involved household incomes per capita are skewed. The population standard deviation can be accepted as being equal to $22,000, based on an earlier study. The prospective developer wants to estimate the true mean annual income per capita in the area. For a random sample of 25 individuals, the mean annual income is found to be $265,000. Using the 95% confidence level, what is the interval estimate of the true mean income per capita in the area?

A. No solution

B. $255,918.84 to $274,081.16

C. $271,376 to $288,624

D. $256,376 to $273,624

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