Reference no: EM13371299

1. There are two basic forms of sleep: slow wave sleep (SWS) and rapid eye movement (REM) sleep. Infants spend about 50% of their sleep time in SWS and 50% in REM sleep. Adults below age 60 spend about 20% of their sleep time in REM and 80% in SWS sleep. In a study of sleep patterns, data was collected on 13 elderly males over age 60. The percentage of total sleep time spent in REM sleep is presented below. 21, 20, 22, 7, 9, 14, 23, 9, 10, 25, 15, 17, 11
(a) Calculate the sample average and standard deviation.
(b) The sample average is how far below 20%?
(c) Calculate the standard error (SE) of the sample average.
(d) The sample average is how many SE's below 20% ?
(e) Is the sample average significantly below 20%, or is it just chance variation?
(f) If you conduct a test of significance on the following hypothesis: `Does the data provide scientific evidence that elderly males spend less than 20% of their sleep time in REM?', how would you write the null and alternative hypotheses?
(g) What is the test statistic you would use?
(i) Calculate a (one-tailed) P-value for your test.
(j) What is the conclusion of your test?

2. Twenty-five factory workers were asked how many vacation days they take a year. The average of the sample was 22.85 days, and the standard deviation of the sample was 5.80.

(a) Calculate the standard error of the sample average.

(b) In the past, the company's Human Resources Office uses an average of 18 vacation days per worker in order to make available man-hour and payroll predictions. Do you think this standard of 18 days needs to be changed? (Is the the observed average of 22.85 significantly different from 18? Calculate a (one-tailed) P-value to measure statistical significance of the difference.)

3. A new breakfast cereal Frosted Corn is test marketed for one month. The total sales for the first 9 quarters (3-month periods) indicate an average of $8350, with a standard deviation of $1840.

(a) Treating the first 9 quarters as a sample of size 9, calculate a standard error for the average sales of $8350.

(b) Based on a cost-profit analysis, production of Frosted Corn will be discontinued if the sample average of the first 9 quarters falls below $9000 with statistical significance. Does the data indicate production will be stopped? (Calculate a one-tailed P-value to measure statistical significance.)

4. A Michigan automobile insurance company would like to estimate the average size of an accident claim for the fiscal year 2002. A random sample of 20 accident claims yielded an average of $1600 with a standard deviation of $800.

(a) What is the standard error of the $1600 estimate?

(b) The national average claim for the industry is $1500. Does the sample indicate that the Michigan average is different from the national average? (Conduct a two-tailed test of significance. What is the P-value of your test?)

5. In order to test a new production method, 15 employees were selected randomly to try the new method. The mean production rate for the sample was 80 parts per hour (with sample SD 10 parts per hour).

(a) Calculate a standard error for the sample mean production rate for the new method.

(b) The mean production rate under the old method is known to be 70 parts per hour. Is the new method rate significantly different, or is this just luck-of-the-draw on the employees sampled ? (Calculate a two-tailed P-value for your test.)