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STATS Questions Assignment




Question;Below are two short answer questions and five true/false questions. Please answer allquestions and send me any work you do in Excel. Also, please bold your answers.Short Answer1. An investor wants to compare the risks associated with two different stocks. One wayto measure the risk of a given stock is to measure the variation in the stocks daily pricechanges. The investor obtains a random sample of 20 daily price changes for stock 1 and20 daily price changes for stock 2. These data are shown in the table below.a. Show how this investor can compare the risks associated with the two stocks by testingthe null hypothesis that the variances of the stocks are equal. Use = 0.10 and interpret theresults of the statistical test.Day1234567891011121314151617181920Price Changefor stock 11.861.801.030.16-0.730.900.090.19-0.420.561.24-1.160.37-0.52-0.091.07-0.880.44-0.210.84Price Changefor stock 20.871.33-0.27- Q-Mart is interested in comparing its male and female customers. Q-Mart would liketo know if its female charge customers spend more money, on average, than its malecharge customers. They have collected random samples of 25 female customers and 22male customers. On average, women charge customers spend $102.23 and men chargecustomers spend $86.46. Additional information are shown below:Summary statistics for two samplesSales (Female)Sample sizes25Sample means102.23Sample standard93.393deviationsTest of difference=0Sample mean differencePooled standard deviationStd error of differencet-test statisticp-valueSales (Male)2286.46059.69515.7779.46623.230.6790.501a. Given the information above, what is and for this comparison? Also, does thisrepresent a one-tailed or a two-tailed test? Explain your answer.b. What are the degrees of freedom for the t-statistic in this calculation? Explain how youwould calculate the degrees of freedom in this case.c. What is the assumption in this case that allows you to use the pooled standard deviationfor this confidence interval?d. Using a 1% level of significance, is there sufficient evidence for Q-Mart to concludethat women charge customers on average spend more than men charge customers?Explain your answer.True or False1. When testing the equality of two population variances, the test statistic is the ratio ofthe population variances, namely.2. Tests in which samples are not independent are referred to as matched pairs or pairedsamples.3. The pooled-variances t-test requires that the two population variances are different.4. In conducting hypothesis testing for difference between two means when samples aredependent (paired samples), the variable under consideration is the sample meandifference between the pairs.5. When the necessary conditions are met, a two-tail test is being conducted to test thedifference between two population proportions. The two sample proportions are and,and the standard error of the sampling distribution of is 0.054. The calculated value ofthe test statistic is 1.2963.Exhibit 6-1Two major automobile manufacturers have produced compact cars with the same sizeengines. We are interested in determining whether or not there is a significant difference inthe MPG (miles per gallon) of the two brands of automobiles. A random sample of eightcars from each manufacturer is selected, and eight drivers are selected to drive eachautomobile for a specified distance. The following data show the results of the test.Driver123456781.Manufacturer B2822272424252827Refer to Exhibit 6-1. The mean for the differences isa.0.50b.1.5c.2.0d.2.5ANSWER:2.Manufacturer A3227262625293125cRefer to Exhibit 6-1. Assuming a 0.05 level of significance, the F-test indicates thata.a t-test assuming unequal variances should be used.b.a t-test assuming equal variances should be used.c.a t-test assuming paired samples should be used.d.the t-statistic > the t-critical value.3.Refer to Exhibit 6-1. The test statistic for determining whether or not there is asignificant difference in the MPG (miles per gallon) of the two brands of automobiles isa.1.616b.1.96c.2.096d.2.2564.Refer to Exhibit 6-1. Assuming a 0.05 level of significance, the null hypothesis (fromnumber 3)a.should not be rejectedb.should be rejectedc.should be revisedd.None of these alternatives is correct.Exhibit 6-2The daily production rates for a sample of workers before and after a training program areshown below.Worker1234567Before20252723222025After222327202519185.Refer to Exhibit 6-2. The null hypothesis to be tested is H0: d = 0. The test statistic isa.-1.96b.1.96c.0.91d.1.6456.Refer to Exhibit 6-2. Thea.null hypothesis should be rejectedb.null hypothesis should not be rejectedc.alternative hypothesis should be acceptedd.None of these alternatives is correct.


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