Download Name Date Ch. 10 – WS #6 Ex 1: Does the job satisfaction of

Name _____________________________________
Ch. 10 – WS #6
Date _________________
Ex 1: Does the job satisfaction of assembly workers differ when their work is machine-paced
rather than self-paced? One study chose 28 subjects at random from a group of women who
worked at assembling electronic devices. Half of the subjects were assigned at random to each of
two groups. Both groups did similar assembly work, but one work setup allowed workers to pace
themselves and the other featured an assembly line that moved at fixed time intervals so that the
workers were paced by machine. After two weeks, all subjects took a survey about job satisfaction.
Then they switched work setups, and took the survey again after two more weeks. The response
variable is the difference in survey scores, self paced minus machine-paced.
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State the parameter of interest.
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Null hypothesis:
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Alternative hypothesis:
Practice: Each of the following situations calls for a significance test for a population mean µ.
State the null hypothesis and the alternative hypothesis in each case.
1. The diameter of a spindle in a small motor is supposed to be 5 mm. If the spindle is either
two small or too large, the motor will not work properly. The manufacturer measures the
diameter in a sample of motors to determine whether the mean diameter has moved away
from the target.
2. Census Bureau data show that the mean household income in the area served by a
shopping mall is $42,500 per year. A market research firm questions shoppers at the mall.
The researchers suspect the mean household income of mall shoppers is higher than that of
the general population.
3. The examinations in a large accounting class are scaled after grading so that the mean
score is 50. The professor thinks that one teaching assistant is a poor teacher and suspects
that his students have a lower mean score than the class as a whole. The TA’s students this
semester can be considered a sample from the population of all students in the course, so
the professor compares their mean score with 50.
4. Last year, your company’s service technicians took an average of 2.6 hours to respond to
trouble calls from business customers who had purchased service contracts. Do this year’s
data show a different average response time?
Ex 2: Back to the sweetness question…
Recall that σ = 1, H0: µ = 0, and Ha: µ > 0. The 10 tasters tested another soda and ended up
with a sample mean of 0.3. Sketch and label a normal curve including this sample mean.
Do we have strong evidence against H0?
Repeat this process with yesterdays sample mean of 1.02. What is the p-value?
Homework
1. Recall the question regarding student attitudes towards school: The Survey of Study Habits
and Attitudes is a psychological test that measures the attitude toward school and study
habits of students. Scores range from 0 to 200. The mean score for US college students is
about 115, and the standard deviation is about 30. A teacher suspects that older students
have better attitudes toward school. She gives the test to 25 students who are at least 30
years of age. Assume that the scores in the population of older students are normally
distributed with standard deviation σ = 30. The teacher wants to test the hypotheses
H0: µ = 115
Ha: µ > 115
Label the curve below according to this situation.
a. Calculate the p-value for x = 118.6.
b. Calculate the p-value for x = 125.7.
c. Which of the two values for x are statistically significant (according to the rule of
thumb)?
2. Recall the question about spending in Cleveland: The Census Bureau reports that
households spend an average of 31% of their total spending on housing. A homebuilders
association in Cleveland believes that this average is lower in their area. They interview a
sample of 40 households in Cleveland metropolitan area to learn what percent of their
spending goes toward housing. Take µ to be the mean percent of spending devoted to
housing among all Cleveland households. We want to test these hypotheses
H0: µ = 31%
Ha: µ < 31%
The population standard deviation is σ = 9.6%. Label the curve below according to this
situation.
a. Calculate the p-value for x = 30.2%
b. Calculate the p-value for x = 27.6%
c. Are these values of x statistically significant (according to the rule of thumb)?
3. Weekly sales of regular ground coffee at a supermarket have in the recent past varied
according to a normal distribution with the mean µ = 354 units per week and standard
deviation σ = 33 units. The store reduces prices by 5%. Sales in the next three weeks are
405, 378, and 411 units. Is this good evidence that average sales are now higher? The
hypotheses are
H0: µ = 354
Ha: µ > 354
Assume that the standard deviation of the population of weekly sales remains at σ = 33.
a. Find the value of the test statistic x .
b. Label the normal curve for the sampling distribution of x when H0 is true.
c. Shade the area that represents the p-value for the observed outcome. Calculate the pvalue.
d. Is the result statistically significant? Do you think there is convincing evidence that
mean sales are higher?
4. A study of the pay of CEOs examined the increase in cash compensation of the CEOs of 104
companies, adjusted for inflation, in a recent year. The mean increase in real compensation
was x = 6.9% and the standard deviation of the increases was s = 55%. Is this good
evidence that the mean real compensation µ of all CEOs increased that year? The
hypotheses are
H0: µ = 0 (no increase)
Ha: µ > 0 (an increase)
Because the sample size is large, the sample s is close to the population σ, so take σ = 55%.
a. Label the normal curve for the sampling distribution of x when H0 is true.
b. Shade the area that represents the p-value for the observed outcome x = 6.9%.
Calculate the p-value.
c. Is the result statistically significant? Do you think the study gives strong evidence that
the mean compensation of all CEOs went up?
5. The financial aid office of a university asks a sample of students about their employment
and earnings. The report says, “for academic year earnings, a significant difference (p =
0.038) was found between the sexes, with men earning more on the average. No difference
(p = 0.476) was found between the earnings of black and white students.” Explain both of
these conclusions for the effects of sex and of race on mean earnings.