**Chapter 7: Sampling & Sampling
Distribution Problems
Part 1: Sampling Text #3, p.
305
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T

2. If the population standard deviation is σ = 8.2 years, compute the standard error (a) with the FPCF and (b) without the FPCF.

Part 1: Estimation for the population mean, µ

One measure of engine performance is fuel efficiency which is usually expressed as miles per gallon (mpg). In a recent study to assess the performance of midsize hybrid cars, the following mpg values were randomly recorded while the car was set to 60 mpg by cruise control.

37.2 | 21.0 | 17.4 | 24.9 | 27.0 | 36.9 | 38.8 | 35.3 | 32.3 | 23.9 |

19.0 | 26.1 | 25.8 | 41.4 | 34.4 | 32.5 | 25.3 | 26.5 | 28.2 | 22.1 |

**1.** What is the point estimate of the population mean mpg?

**2.** What is the standard error of the estimator? Interpret its
meaning.

**3.** Assuming that the population of the highway readings of hybrid cars is
normally distributed,

**a.** what is the 95% margin of error?

** b. **develop a 95% confidence interval for the population mpg.

** c.** Suppose a sticker information on a midsize hybrid
vehicle states a higher average mpg of 27 (manufacturer's claim), are your
results consistent with the manufacturer's claim? Explain.**
Part 2: Estimation for the Population proportion, P**.

A congressional committee was recently charged with estimating the percentage of adult Americans without health care insurance coverage. The committee conducted a sample survey and found that 87 out of 562 adult Americans did not have health care insurance. Use this information to answer these questions.

1. Define the variable X, the random variable of interest for this problem?

2. At 95% confidence, what is the margin of error?

3. What is the 95% confidence interval for the proportion of adult Americans without health care insurance coverage?

4. Briefly, write a report of your findings to the congressional committee that paid you for the study.

(Please, be sure to state H

Part 1: Hypothesis Testing about the Population Mean,

Which is cheaper: eating out or dining in? The mean cost of dining in by cooking steak, broccoli and rice bought at a grocery store is $13.04 according to Money.msn website (2012). A sample of 100 neighborhood restaurants showed a mean price of $12.75 and a standard deviation of $2 for a comparable restaurant meal.

1. State the appropriate null and alternative hypotheses for a test to determine whether the sample data support the conclusion that the meal cost of a restaurant meal is less than fixing comparable meal at home.

2

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**Copyright© 1996, Ebenge Usip, all rights reserved.
Last revised:
Tuesday, May 18, 2021.**