Question

Assume that we want to construct a confidence interval. Do one of the following, as appropriate:

(a) find the critical value tx/2.
(b) find the critical value 29/2, or (0) state that neither the normal distribution nor the distribution applies, Here are summary statistics for randomly selected weights of newborn girls: n=274, X= 33.7 hg, s= 7.7 hg. The confidence level is 90%. Select the correct choice below and, if necessary, fill in the answer box to complete your choice 62-0 (Round to two decimal places as needed.) B 20/2- (Round to two decimal places as needed)
(c) Neither the normal distribution nor the distribution applies

Answer 1

To construct a 90% confidence interval for the weights of newborn girls, we can use a t-distribution with a critical value of 1.645 and calculate the standard error. The confidence interval is (32.937, 34.463) hg.

Step-by-step explanation:

To construct a 90% confidence interval for the weights of newborn girls, we first need to find the critical value. Since the sample size is large (n > 30) and the population standard deviation is unknown, we can use a t-distribution. The critical value for a 90% confidence interval with 273 degrees of freedom is approximately 1.645.

Next, we calculate the standard error (SE) using the formula SE = s / sqrt(n), where s is the sample standard deviation and n is the sample size. In this case, SE = 7.7 / sqrt(274) = 0.464.

Finally, we can calculate the confidence interval by adding and subtracting the margin of error from the sample mean. The margin of error is obtained by multiplying the critical value by the standard error: margin of error = 1.645 * 0.464 = 0.763. Therefore, the 90% confidence interval for the weights of newborn girls is (33.7 - 0.763, 33.7 + 0.763) or approximately (32.937, 34.463) hg.