Question

Question Help Use the one-standard deviation ?-test and the one-standard deviation je interval procedure to conduct the required hypothesis tout and obtain the specified confidence interval for a sample of on-25 wa standard deviation of s7 a. Hy 5, H > 5,0 -0.025 b. 95% confidence interval Click the icon to view a portion of the y distribution table. a. Compute the test statistic (Round to three decimal places as needed.) Find the critical value(s) (Round to three decimal places as needed. Use a comma to separate answers as needed) Make a conclusion based on these results. Choose the correct answer below O A Reject H. The test statistic is greater than or equal to the critical value OB. Do not reject Ho. The test statistic is less than the critical value OC. Do not reject H The test statistic is greater than or equal to the critical value OD Raject Ho. The test statistic is less than the critical value Click to select your answers)

Answer 1

Given that, s = 7,n= 25 Null hypothesis: H.:0=5 Alternative hypothesis: H:0 > 5 Level of significance, a = 0.025 Test statistic: (n-1) s? o (25-1) 72 52 = 47.040 Degree of freedom: n - 1 = 25-1 =24 x² Critical value: Using the chi square table, the critical value at a = 0.025 for a right tailed test is, X.025 = 39.364 Decision rule: Reject H , if x² > xã otherwise do not reject H.. Since the test statistic is greater than the critical value, so we reject the null hypothesis at 5% significance level. Hence, the correct answer is option (A)

b) By using the chi square table, the critical values at 5% level of significance are Xi =12.401, x2 = 39.364 The 95% confidence interval for standard deviation is, n- - 1)s (n-1)s 95%CI= Xú x (25-1) 7 (25-1)72 39.364 V 12.401 = 5.465803939<o<9.738124 = 5.466<o<9.738