Question

A random sample of 20 recent weddings in a country yielded a mean wedding cost of $26,387.22. Assume that recent wedding costs in this country are normally distributed with a standard deviation of $8400. Complete parts (a) through (c) below. a. Determine a 95% confidence interval for the mean cost, u, of all recent weddings in this country. The 95% confidence interval is from $to $ (Round to the nearest cent as needed.) b. Interpret your result in part (a). Choose the correct answer below. O A. We can be 95% confident that the mean cost, p, of all recent weddings in this country is somewhere within the confidence interval. O B. We can be 95% confident that the sample cost of recent weddings in this country is somewhere within the confidence interval. O C. The mean cost, u, of all recent weddings in this country is somewhere within the confidence interval. OD. We can be 95% confident that any randomly selected recent wedding cost in this country is somewhere within the confidence interval. c. Does the mean cost of all recent weddings in this country lie in the confidence interval obtained in part (a)? Explain your answer. O A. The population mean may or may not lie in this interval, but we can be 95% confident that it does. B. The sample mean may or may not lie in this interval, but we can be 95% confident that it does. OC. Yes, since the confidence interval must contain the sample and population means. OD. No, since there is a 5% chance that the population mean does not lie in the confidence interval.

Answer 1

CI=(22706 , 30069)

Solution: The provided sample mean is X = 26387.22 and the population standard deviation is o = 8400. The size of the sample is n = 20 and the required confidence level is 95%. Based on the provided information, the critical z-value for a = 0.05 is ze = 1.96. The 95% confidence for the population mean u is computed using the following expression CI (* Zexo Zcxo Vn Therefore, based on the information provided, the 95% confidence for the population mean u is CI = ( 26387.22 1.96 x 8400 ,26387.22 + V20 1.96 x 8400 20 (26387.22 - 3681.395, 26387.22 + 3681.395) = (22705.825, 30068.615)

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(6) option.(A) We can be 95% confident that the mean Cost, M, of all recent weddings in this county is somewhere within the confidence interval, C CSI option.(A) The population mean may or may not lie intis. Interval, but cae can be 95% confident that it does