# STAT 101 Statistic Problems Paper

• 1/ Various temperature measurements are recorded at different times for a particular city. The mean of 20ºC is obtained for 40 temperatures on 40 different days. Assuming that σ=1.5ºC, test the claim that the population mean is 22ºC. Use a 0.05 significance level.

Identify the null hypothesis, alternative hypothesis, test statistics, P-value and final the conclusion about the original claim.

• 2/ A random sample of 16 women resulted in blood pressure levels with a standard deviation of 22.7 mm Hg. A random sample of 17 men resulted in blood pressure levels with a standard deviation of 20.1 mm Hg.

Use a 0.05 significance level to test the claim that blood pressure for women vary more than blood pressure levels for men.

• 3/ A manufacturer considers his production process to be out of control when defects exceed 3%. In a random sample of 85 items, the defect rate is 5.9% but the manager claims that this is only a sample fluctuation and production is not really out of control. Identify the null hypothesis, alternative hypothesis, test statistics, P-value and At the 0.01 level of significance test the manager claim.
• 4/ A researcher was interested in comparing the response times of two different cab companies. Companies A and B were each called at 50 randomly selected times. The calls to company A were made independently of the calls to company B. The response times for each call were recorded. The summary statistics were as follows:
 Company A Company B Mean response time 7.6 mins 6.9 mins Standard deviation 1.4 mins 1.7 mins

Use a 0.01 significance level to test the claim that the mean response time for company A is the same as the mean response time for company B. Use the P-value method of hypothesis testing.

• 5/ A coach uses a new technique to train gymnasts. 7 gymnasts were randomly selected and their competition scores were recorded before and after the training. The results are shown below
 Subject A B C D E F G Before 9.6 9.7 9.7 9.4 9.7 9.5 9.5 After 9.7 9.9 9.7 9.3 9.8 9.8 9.3

Using a 0.01 level of significance, test the claim that the training technique is effective in raising the gymnasts’ score.

Use the traditional method of hypothesis testing with critical value t= -3.143.

• 6/ Test the claim that the mean lifetime of car engines of a particular type is greater than 2,20,000 miles. Sample data are summarized as n=23, x~ = 2,26,450 miles and s=11,500 miles . Use a significance level of a= 0.01

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Thank you