Question

In class we had 41 95% confidence intervals that we believe to be calculated correctly. The confidence intervals were collected by taking a sample of 60 data points from the population data. 41 of the confidence intervals appear to be calculated correctly. Of these 4 of them do not have the population mean inside the confidence interval. Based on a 95% confidence, we expected 2 to not contain the population mean. Did this happen by chance alone? To find your answer, complete the 7 steps of hypothesis testing and compute Beta.

This was my data:

Your Sample Mean Your Sample Standard Deviation Lower 95% Confidence Interval Upper 95% Confidence Interval Is the population mean inside your confidence interval? n=5 25115.8 12802.781 13893.668 36337.932 1 n=15 15037.467 13487.498 8211.851 21863.083 1 n=30 22562.067 19342.967 15640.275 29483.859 1 n=60 17956.533 17475.229 13534.69 22378.376 1

    

Answer 1

test for being Answers Summarized the information given in problem; As we are tecting here whether the true Ci confidence level hare is 95%, therefore this is a proportion equal to 0.95. The sample proportion here is computed as; P = (41-4)/61 0.902h. -> As we are testing here whether the confidence level is 0.95, therefore the test statistic here is computed as: 0.90241-0.95 -1.3973 0.05 (0.05) P-P P (1-P) 01 a AS this is one tailed test, we have the p-value from standard normal tables here as; pa P(za <-1.3973) 2x 0-0812 = 0.10214 As the p-value here is 0.0812 > 0.05 therefore that is not an unusual event for 5% level of significance here, therefore we cannot Beject the null- hypothesis.

Therefore this can happen by chance alone At 5% level of significance we don't have suffecient evidence here that the confidence level is not equal to 95% here. ** Please please kindly Up-vote. Thank you in advance.