4. A sports shoe manufacturer claims that joggers who wear its brand of shoe wil

Question

4. A sports shoe manufacturer claims that joggers who wear its brand of shoe wil jog faster than those who don't use its product. A sample of eight joggers is taken, and the joggers agree to test the claim on a 1-mile track. The rates (in minutes) of the joggers while wearing the manufacturer's shoe and while wearing any other brand of shoe are shown here. Test the claim that the manufacturer's brand improves speed. Other Brand 6.3 9.2 8.6 6.8 Manufacturer's Brand 6.8 8.0 5.8 8.0 8,0 5. A medical researcher wishes to see whether the pulse rates of smokers are higher than the pulse rates of non-smokers. Samples of 100 smokers and 100 non-smokers are selected. The results are shown below. Can the researcher conclude that smokers have higher pulse rates than non-smokers. We will assume equal population variances. Non-smokers S a 5 S. 6 6. A college admissions officer believes that students enrolling from Shawnee school District have higher SAT scores than those who enroll from West River School District. A sample of 30 students from each district is selected. The average SAT score for these students in the Shawnee district is 656 with a standard deviation of 100, The average SAT score for these students West River district is 560 with a standard deviation of 90 Is the belief of the admissions officer substantiated? 7. In order to determine rates, a motel manager wishes to find the 90% confidence interval of the mean rate that competing motels charge. He wishes to be accurate ithin $2. If the standard deviation of the rates is $10, how large a sample must be selected to get the desired information? A national magazine claims that the average college student watches less television than the general public. The national average is 29.4 hours per week, with a standard deviation of 6 hours. A sample of 45 college students has a mean of 28 hours. a. Test the hypothesis that the average college student watches less television than the general public. b. For which of the following significance levels can the null hypothesis be rejected? 20 None of these a w 05 .01 a 02 c. Test the hypothesis that the average college student watches a different amount of television than the general public. d. For which of the following significance levels can the null hypothesis be rejected? 20 None of these a 05 e. Test the hypothesis that the average college student watches more television than the general public. For which of the following significance levels can the null hypothesis be rejected? None of the a .05 a 3.02 .01

Explanation / Answer

Here we assume population standard deviation is inknown.

Using Minitab,

Two-Sample T-Test and CI: manufactures brand, other brand

Two-sample T for manufactures brand vs other brand

N Mean StDev SE Mean
manufactures brand 8 7.84 1.05 0.37
other brand 8 7.61 1.16 0.41

Difference = (manufactures brand) - (other brand)
Estimate for difference: 0.225
95% upper bound for difference: 1.205
T-Test of difference = 0 (vs <): T-Value = 0.41 P-Value = 0.655 DF = 13

the t-value is 0.41 and the associated p-value is 0.655. When Minitab displays a p-value of 0.655, iP-value >0.05 so we do not reject null hypothesis and we conclude that manuctaures brand improve speed than other brand.

Hope this will help you. Thanks

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