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1 Hypothesis testing *Use the 5% level of significance for all the following tests. 1. Hypothesis testing for when 2 is known. a) A random sample of size 100 is taken and X =8. Test H0 . *Use z-score because sample size is large, this is a two-tail test. b) A random sample of size 100 is taken and X =10.5. Test H0 . *This is a one-tail test. 2. Hypothesis testing for  when 2  is unknown (we can only calculate 2 s from the sample). A random sample of size 36 is taken. The sample mean is 148 and the sample variance is 81. Test H0 *Sample size is small so use t-score 2 3. Hypothesis testing for  when 2  is unknown, and the sample size is small. The current rate for producing 5 amp fuses at Neary Electric Co. is 250 per hour on average. A new machine has been purchased and installed. According to the supplier, it will increase the production rate. A sample of 10 randomly selected hours from last month production reports the following production numbers: 245, 254, 259, 240, 257, 280, 258, 278, 290 and 241 fuses per hour. *This is a one tail test. 1) Calculate sample mean; 2) Calculate sample standard deviation; 3) Calculate standard error; 4) Based on above information, perform a hypothesis test that answers the following question: At the .05 significance level can Neary conclude that the new machine is faster than 250 per hour? 4. We ran a regression on college GPA using high school GPA as the only independent variable. The coefficient for high school GPA and its standard error are reported in the table below (ignore the intercept; n=141). Coefficients Standard Error Intercept 1.415434 0.306938 hsGPA 0.482435 0.089826 a) At .05 level, test the hypothesis that the coefficient of ‘hsGPA’ is equal to ‘0’. Can you reject or not reject the null? Show your steps. *This is a two-tail test. b) At .01 level, test the hypothesis that the coefficient of ‘hsGPA’ is positive (greater than ‘0’). Can you reject or not reject the null? Show your steps. *This is a one-tail test. c) What can you conclude from above hypotheses testing results?

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