Find the confidence interval for population mean

Reference no: EM1321306

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 probability 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. Use the population standard deviation along with the sample mean, S, and find a 92% confidence interval for the population mean. Is the true population mean contained in this interval?

c. Assume that the population standard deviation is unknown. Use S to find a 94% confidence interval for the population mean. Is the true population mean contained in this interval?

d. Use the population standard deviation and determine how many woman you would need to sample to ensure that you are 93% confident that the sample mean is within 3 pounds of the population mean.

Reference no: EM1321306

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