Find the Confidence interval for population mean.
The following 80 observations represent the population of weights in pounds of women in a statistics class. You are to assume that it is normally distributed.
Row 1: 123, 120, 121, 117, 117, 124, 109 124, 124, 124, 112, 119, 125, 124, 118, 129, 126, 112, 121, 120
Row 2: 124, 112, 121, 120, 117, 122, 122, 117, 117, 125, 125, 121, 131, 127, 116, 123, 130, 117, 120, 114
Row 3: 119, 123, 118, 122, 116, 116, 121, 113, 119, 127, 117, 124, 118, 117, 127, 122, 122, 119, 114. 121
Row 4: 121, 122, 123, 124, 125, 126, 127, 128, 128, 129, 130, 131, 130, 129, 129, 126, 130, 133, 131, 132
Let Row 3 represent a random sample of 20 women from the population. Let S=the sample mean of the 20 weights from Row 3.
a. What is the likelihood of observing a sample mean weight from any 20 women selected from this population that is greater than S using the population standard deviation?
b. utilize the population standard deviation along with the sample mean, S, and find a 92 out confidence interval for the population mean. Is the true population mean contained in this interval?
c. suppose that the population standard deviation is unknown. Utilize S to find a 94 out confidence interval for the population mean. Is the true population mean contained in this interval?
d. make use of the population standard deviation and determine how many woman you would need to sample to ensure that you are 93 out confident that the sample mean is within 3 pounds of the population mean.