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, Pvalue 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, Pvalue 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 Pvalue 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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