The 95% confidence interval for the population mean , given that the sample size n = 49 and the population standard deviation = 7, is .

Question

The 95% confidence interval for the population mean  , given that the sample size n = 49 and the population standard deviation  = 7, is  .

Quizplus · Accepted Answer

Since we know the sample size (n = 49), population standard deviation (σ = 7), and have calculated the sample mean (x̄ = 11eb06d9_cc00_da92_8177_fdc019156a15_TB1387_11), we can use the formula for a t-distribution to calculate the 95% confidence interval. Assuming a large enough sample size, the t-distribution approaches the normal distribution, and we can use the z-score for the 95% confidence level, which is approximately 1.96. Therefore, the 95% confidence interval can be calculated as:

x̄ ± z*(σ/√n)

= 11eb06d9_cc00_da92_8177_fdc019156a15_TB1387_11 ± 1.96*(7/√49)

= 11eb06d9_cc00_da92_8177_fdc019156a15_TB1387_11 ± 1.96

= (11eb06d9_cc00_db3f_8177_0358a96b70ce_TB1387_11, 11eb06d9_cc00_d96e_8177_b7e360f55896_TB1387_11)

Therefore, the given statement is true and the answer is A.

The 95% Confidence Interval for the Population Mean