Statistics Quiz – Due Today

1. Hoping to lure more customers to the downtown area, the city council has voted to build a new

parking garage. They plan to pay for the garage using parking fees. In order to determine what

the fees at the new structure should be, the daily fees collected during a three month period

(66 weekdays) at another parking facility averaged $126 with a standard deviation of $15.

a. Construct a 95% confidence interval for the average daily parking fees.

b. The consultant, who advised the city on this project, predicted that the parking revenues would average $130 per day. Based on your confidence interval, do you think the consultant was correct? Explain.

2. Twenty-five volunteers who had developed cold symptoms within the last 24 hours were given zinc lozenges to take every 2 to 3 hours until their cold symptoms were gone. The mean overall duration of symptoms was 4.5 days with a standard deviation of 1.6 days.

The selected cases have a distribution which appears to be symmetric and bell-shaped.

a. Construct a 99% confidence interval for the mean overall duration of symptoms in a

population of individuals who used zinc lozenges.

b. In a previous test, the mean overall duration of symptoms for volunteers who were

told to drink an herbal tea for relief of their symptoms was 7 days. Based on your

confidence interval, do you think that using the lozenges reduces the overall duration

of symptoms compared to using the herbal tea?

For the following problems:

1. State the Null Hypothesis and the Alternative Hypothesis

2. Determine the test statistic.

3. Determine the P-value

4. Make a decision regarding the hypotheses based on the P-value and the Level of

Significance.

3. In order to monitor the ecological health of the Florida Everglades, various measurements are recorded at different times. The bottom temperatures are recorded at the Garfield Bight station and a mean temperature of 30.4°C is obtained for the temperatures recorded on 61 different days. Assuming that σ = 1.7°C, test the claim that the mean population temperature is greater than 30.0°C. Use a 5% level of significance.

4. Patients with Chronic Fatigue Syndrome were tested, and then retested after being treated with fludrocortisone. The changes in fatigue after treatment were measured (based on data from “The Relationship between Neurally Mediated Hypotension and the Chronic Fatigue Syndrome” by Bou-Holaigah, Rowe, Kan, and Calkins, Journal of the American Medical Association, Vol.274, No. 12). A standard scale from -7 to +7 was used with positive values representing improvements. The sample of 21 patients had a mean score of 4 on the scale with a sample standard deviation, s = 2.17 Use a 1% level of significance level to test the hypothesis that the mean change is positive(i.e. there is improvement.). Does the treatment appear to be effective?

5. A survey taken showed that among 785 randomly selected subjects who completed 4 years
of college, 144 smoke and 641 do not smoke (based on data from the American Medical
Association). Use the 0.01 level of significance to test the claim that the rate (proportion) of
smoking among those with four years of college is less than 27 out of 100 rate of the general
public. Why do you think that the rate of college graduates who smoke would be less than the
rate of the general public?