Mind On Statistics - Chapter 13 Worksheets With Answers Page 27
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32Chapter 13
130. A biologist wants to measure the effect of a fertilizer on the growth of roses. She plants 20 roses in 10 plots
of land with 2 roses in each plot. She randomly applies the fertilizer to one of the two roses in each plot, and
then compares the average height of the roses with fertilizer to the average height of roses without fertilizer
after 1 month. What is the appropriate statistical procedure she should use?
KEY: The study design is a paired design, so a paired t-procedure could be used, provided the assumption of
normality for the height of roses is reasonable. She would probably want to compute a confidence interval for
the average difference in the population of roses like these. She might also want to test to see if the population
mean difference is greater than 0, with fertilized roses growing taller.
131. A researcher wants to assess if the time of day during which one works affects job satisfaction. A study
compared job satisfaction for day-shift nurses versus night-shift nurses. Independent samples of nurses from
each group were obtained and their job satisfaction was measured on a numerical scale with higher scores
indicating greater satisfaction. Identify the appropriate parameter for this situation and name an appropriate
technique that might be performed provided the underlying assumptions are met.
KEY: Since the response is quantitative and there are two independent samples, the appropriate parameter would be
the difference between two population means
where
is the mean job satisfaction for day-shift
1
2
1
nurses and
is the mean job satisfaction for night-shift nurses. A potential test is the two independent
2
samples t-test.
132. A study will be conducted to compare the proportion of earth-quake insured residents between two counties.
Surveys will be mailed to a sample of residents in each county. The results will be used to assess if the county
that is closer to a major earthquake fault has a higher proportion of residents with such insurance. Identify the
appropriate parameter for this situation and name an appropriate technique that might be performed provided
the underlying assumptions are met.
KEY: Since the response is categorical and there are two independent samples, the appropriate parameter would be
the difference between two population proportions p
- p
where p
is the proportion of residents with such
1
2
1
insurance in county 1 and p
is the proportion of residents with such insurance in county 2. A two
2
independent samples z-test would be performed provided the samples are representative and the sample sizes
are sufficiently large.
133. A company is interested in estimating the mean number of days of sick leave taken by all its employees. The
firm’s statistician selects a random sample of personnel files, notes the number of sick days taken by each
employee over previous year. Identify the appropriate parameter for this situation and name an appropriate
technique that might be performed provided the underlying assumptions are met.
KEY: Since the response is quantitative and there is one sample, appropriate parameter would be the population
mean
, the mean number of days of sick leave for the population of all employees. A potential technique is
a one-sample t confidence interval for estimating the population mean.
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