STAT 2023 1. Using the given statement find the p-value: a) Test statistic z = 1.50 is obtained when testing the claim that H1: p 0.25 A) 0.2884 B) 0.1336 C) 0.6331 D) 0.448 b) With H1 : p < 0.6, the test statistics is z = -3.00 A) 0.0013 B) 0.0423 C) 0.1033 D) 0.6551 2. A random sample of 500 observations produced a sample proportion equal to 0.38.show the critical region and the corresponding critical values of the following test of hypotheses using = 0.05. a) H0 : p = 0.30 H1 : p > 0.30 b) H0 : p = 0.30 H1 : p 0.30 3. Consider the null hypothesis H0: p = 0.25. Using = 0.01, show the rejection regions and the corresponding critical value for a: a) Left-tailed test b) Two-tailed test c) Right-tailed test 4. Consider = 0.01, H0 : p = 0.70 H1 : p 0.70 a) A random sample of 600 observations produced a sample proportion equal to 0.68. Find the test statistic: A) 2.077 B) -1.053 C) -2.036 D) 1.833 b) Would you reject the null hypothesis at = 0.01 significance level? A) Yes, reject H0 B) No, fail to reject H0 c) Would you reject the null hypothesis at = 0.001? A) Yes, reject H0 B) No, fail to reject H0 5. According to the American Diabetes Association, 23.1% of Americans aged 60 years or older had diabetes in 2007. A recent random sample of 200 Americans aged 60 years or older showed that 52 of them have diabetes. Using = 0.05 significance level, perform a test of hypothesis to determine if the current percentage of Americans aged 60 years or older who have diabetes is higher than that in 2007. a) Find the test statistic: b) The p-value for this test is: c) What do you conclude? A) 0.882 B) 0.771 C) 0.967 A) 0.166 B) 0.227 C) 0.095 A) Reject H0 B) Fail to reject H0 D) 0.228 D) 0.662 6. For the following hypothesis tests: =5 a) Find the test-statistic 'z ' b) Find the p-value: H0 : = 23, H1 : 23, n = 50, sample mean = 21.25, A) 1.889 A) 0.6874 B) -3.623 B) 0.0132 C) 2.422 C) 0.0051 D) -2.475 D) 0.2231 7. Consider Ho: = 72 versus H1: > 72. A random sample of 16 observations taken from this population produced a sample mean of 75.2. The population is normally distributed with = 6. a) Find the test-statistic: b) Calculate the p-value A) 2.133 A) 0.3351 B) 2.883 B) 0.0166 C) 1.223 D) 3.002 C) 0.3522 D) 0.2214 c) Consider the p-value of part b), would you reject the null hypothesis if the test were made at the significance level of 0.01? A) Yes, reject H0 B) No, fail to reject H0 8. For each of the following examples of test of hypothesis about , show the rejection region including the corresponding critical value(s). a) A two tailed test with = 0.01 b) A left-tailed test with = 0.005 c) A right-tailed test with = 0.025 9. The manufacturer of a certain brand of auto batteries claim that the mean life of these batteries is 45 months. A consumer protection agency that wants to check this claim took a random sample of 30 such batteries and found that the mean life for this sample is 43.05 months. The lives of all such batteries have a normal distribution with the population standard deviation of 4.5 months. a) Find the p-value to test the hypothesis that the mean life of these batteries is not 45 months. A) 0.0174 B) 0.1133 C) 0.2238 b) Will you reject the null hypothesis at = 0.03? A) Yes, the null hypothesis is rejected D) 0.0317 B) No, fail to reject the null hypothesis c) For what significance level ' ' could you fail to reject the null hypothesis? A) 0.055 B) 0.025 C) 0.018 D) 0.001