Question

1. Suppose we measure the heights of 40 randomly chosen statistics students. We find a mean height of 175cm. Since we have a sufficiently large sample, let’s just assume that the sample standard deviation is the same as the population standard deviation = 20cm.

1. Construct a 95% confidence interval for the population mean height of statistics students AND write a sentence interpreting your results.
2. Construct a 99% confidence interval for the population mean height of statistics students AND write a sentence interpreting your results.

2. There are hundreds of apples on the trees (seriously, this was supposed to be a nice fall example, then it snowed!), so you randomly pick 46 apples and get a mean circumference of 86 and a standard deviation of 6.2 mm.

1. Construct a 90% confidence interval for the size of the apples and write a sentence interpreting your result.

2. If the orchard’s contract with Pick-n-Save states that apples must be 88mm in circumference or larger, are you in trouble? Explain.

Answer 1

The confidence interval shows that we are 90% confident that the apples will have mean circumference in the interval (84.46, 87.53). But pick n save states that the mean circumference should be equal to or larger than 88. So there is trouble because the mean circumference would not be greater than 87.53