Problem 5E

Recently many companies have been experimenting with telecommuting, allowing employees to work at home on their computers. Among other things, telecommuting is supposed to reduce the number of sick days taken. Suppose that at one firm, it is known that over the past few years employees have taken a mean of 5.4 sick days. This year, the firm introduces telecommuting. Management chooses a simple random sample of 80 employees to follow in detail, and, at the end of the year, these employees average 4.5 sick days with a standard deviation of 2.7 days. Let µ represent the mean number of sick days for all employees of the firm.

a. Find the P-value for testing H0: µ ≥ 5.4 versus H1:. µ< 5.4.

b. Do you believe it is plausible that the mean number of sick days is at least 5.4, or are you convinced that it is less than 5.4? Explain your reasoning.

REPORTING DESCRIPTIVE DATA ● Should be accurate, concise, and understandable Frequency Distributions ● Summarizes raw data by showing the number of scores that fall in each of several categories ● Simple frequency: number of participants who obtained each score ● Raw scores: arrange raw scores from lowest to highest ○ Count the frequency of each score ● Simple frequency distribution:um of frequency of scores should total sample size in study ○ Histogram: frequency column on y-axis and scores on x-axis ■ Arrange from low to high ● Grouped frequency: subsets of scores ○ Ensure equal intervals ○ Same histogram format ● Mean: average ● Median: middle number ● Mode: most frequent number Measures of Variability ● Range: least useful ● Variance: average extent to which scores in a data set deviate from the mean (squared units, not easy to interpret) ● Standard deviation:square root of variance (original units of data) ● Standard deviation and variance ○ On average, how far are scores from the mean ○ High vs. low variability ● Normal distribution:normal curve ○ Most of the scores fall around the mean while fewer and fewer fall into the low and high end of the distribution ○ People are about average with only a few falling outside the norm ○ 68% are within 1 SD of the mean ■ 95% within 2 SD ■ 99% within 3 SD Skewed distributions ● Negative: most of the scores cluster at the higher end with a few outliers around the bottom ● Positive: most of the scores cluster at the lower end with a few outliers toward the top Z-Scores ● Identifies where a participant’s score falls in relation to the other participants ● Tells us how far a particular score is from the mean in standard deviation units Xi = participant’s score X = mean of the sample S = standard deviation of the sample