I. Confidence Intervals (use Excel or SPSS for descriptive statistics and include your output)

The US Department of Transportation reported the number of miles that residents of metropolitan areas travel per day in a car. Suppose a simple random sample of 15 residents of Cleveland provided the following data on car miles per day:

20, 20, 28, 16, 11, 17, 23, 16, 22, 18, 10, 22, 29, 19, 32

(Note: Use SPSS or Excels Data Analysis to compute your descriptive statistics (e.g. sample mean, standard deviation).

a) Compute a 95% confidence interval estimate of the population mean number of miles residents of Cleveland travel per day in a car. Write down the confidence interval, showing the lower and upper bound. Interpret the confidence interval. (i.e. what does it mean).

b) Did you use t or z for the critical value? Why?

c) What is the value of the margin of error for your confidence interval?

d) Suppose it is desirable to estimate the population mean number of miles with a margin of error of plus/minus 2 miles. Does the sample data above provide that level of precision? If not, what sample size would you have to draw to give you that precision level?

II. Hypothesis Testing (do this by hand)

The monthly rent for a two-bedroom apartment in a particular small town is reported to equal $550. Suppose we want to test whether that reported figure is correct. We draw a sample of 36 two bedroom apartments and calculate the mean monthly rent of the sample to be $562 and the sample standard deviation to be $40. Use this sample to determine if the true average monthly rent is different from what was reported.

a) What are the null and alternative hypotheses? Explain your answer.

b) Using the critical value method, now conduct this hypothesis test at the 5% level of significance.

i) What is the critical value? Did you use the z or the t statistic to determine the critical value? Why?

ii) What is the value of the test statistic?

iii) What is your conclusion? Do you reject the null or not? Explain why.

iv) Draw a picture of the sampling distribution of the sample mean illustrating your hypothesis test. (i.e. show the critical value, the test statistic, the rejection range, etc).

c) What is the p-value?