Recitation 12

Tests and Intervals for Normal Population Means

1.

An automobile manufactured wants to advertise a model as achieving 30 mi/gal on average in real highway driving conditions. To assess fuel efficiency, six non-professional drivers are selected and each one drives a car from Phoenix to Los Angeles. The resulting miles per gallon figures are

27.2

29.3

31.2

28.4

30.3

29.6

The sample average is 29.33 and the sample standard deviation is 1.41.

(a)

Describe in words the population and the average $\mu$ of the population that is being studied.

(b)

Find a 95% confidence interval for $\mu$.

(c)

The manufacturer wishes to test the hypothesis that $\mu = 30$ mi/gal against the alternative that $\mu < 30$ mi/gal. Compute the p-value for this test and describe in words what it means.

(d)

Suppose the p-value is around 0.16, thus not statistically significant at the most commonly used levels. Based on this result, the manufacturer want to state in their advertising literature that their claim of a 30 mi/gal fuel efficiency was confirmed by statistical analysis. Is this appropriate? Justify your answer.

(e)

What assumptions are required for the methods you used? How would you try to decide whether those assumptions are appropriate?

2.

A study measured the systolic blood pressure of a random sample of 101 diabetic males aged 35-44 living in the United States. The sample mean was 130 with sample standard deviation of 8.

• Find a 90% confidence interval for the mean systolic blood pressure of all diabetic males aged 35-44 in the United States.
• The mean systolic blood pressure for all males aged 35-44 in the United States is 127.2. Does the sample provide evidence that the mean for diabetics is differs from that of the entire population?