Given that n = 49, = 75, and = 7, the lower and upper limits of the 68.26% confidence interval for the population mean are 74 and 76, respectively.

Question

Given that n = 49,  = 75, and  = 7, the lower and upper limits of the 68.26% confidence interval for the population mean  are 74 and 76, respectively.

Quizplus · Accepted Answer

The given information implies that we have a sample mean of 75 with a sample size of 49, and we want to construct a 68.26% confidence interval for the population mean. Since the sample size is large (n≥30), we can use the z-distribution for the confidence interval. The formula for the confidence interval is:

x̄ ± z* (σ/√n)

where x̄ is the sample mean (75), σ is the population standard deviation (unknown in this case), n is the sample size (49), and z* is the critical value that corresponds to the desired confidence level (68.26% in this case).

Using a z-table, we find that the critical value for a 68.26% confidence interval is approximately 1. Therefore, the confidence interval is:

75 ± 1*(σ/√49)
= 75 ± σ/7

We are given that 11eab386_b92d_88d3_aec0_17845e56f1da_TB4962_11 = 7, which corresponds to the sample standard deviation of the data set. Therefore, we can estimate σ as 7/0.9949 ≈ 7.04. Substituting this value into the formula, we get:

75 ± 7.04/7
= 75 ± 1.006

The lower and upper limits of the confidence interval are therefore 74 and 76, respectively. Since these are the same as the ones given in the statement, the answer is true.

Given That N = 49, = 75, and