1. Hotels often leave questionnaires concerning the quality of their service in the hotel rooms and ask the guests to fill them out. Do the results from such a procedure constitute a random sample? Why or why not ?
[answer]
2. Describe what types of error or bias (if any) is likely in the following situation:
(a) An interviewer is told to contact 50 randomly selected families as part
of a large survey to determine the average income in a community. The
interviewer contacts the families that live in the nice section of town and
reports that the other families could not be contacted.
(b) A radio announcer asks listeners to call the show to give their opinion
about a controversial subject.
[answer]
3. A student adviser wants to estimate the mean annual income of all university students who graduated last year. The population standard deviation is believed to be $2000. Based on a random sample of 25 graduates, the advisor obtains = $24,500.
(a) Construct a 95% confidence interval for the unknown population mean f.
(b) Construct a 99% confidence interval for f and compare it to the answer in (a)
[answer]
4. A random sample of 100 working people participated in a survey of workforce characteristics. The mean age for the sample was = 36.4 years. From previous surveys it is known that s = 11 years. Find a 95% CI for µ, the population mean age of the workforce.
5. Consider this statement: The percentage of people at work who were smoking fell significantly (2-sided p=0.02) from 4.2% in March to 3.7% in April.
[answer]
6. For the following situation, indicate in each case whether a correct decision has been made, or whether a Type I or Type II error has occurred. The null and alternative hypotheses are:
[answer]
7. A management firm would like to estimate the mean cost of repairing damage to apartments that are vacated by tenants. A sample of 26 vacated apartments resulted in a sample mean repair cost of $116 with a sample standard deviation of $12. Develop a 95% confidence interval to estimate the mean repair cost for the population of apartments.
[answer]
8. Two manufacturing companies produce carbide drill tips that are used to cut holes in steel sheets. A customer wishing to know which drill tips have the longer life purchases independent samples of n1 = 20 drill tips from Company 1 and n2 = 15 drill tips from Company 2. The mean lives of the drill tips are = 78 minutes and = 84 minutes. The population variances are unknown but assum ed to be equal. The sample variances are s= 41 and s= 36. Construct a 95% conf idence interval for (f1 - f2).
[answer]
9. A researcher honestly believes that a new medication reduces blood pressure. However, a test on five people did not show a significant average reduction in blood pressure. Is it still possible that the medication is effective, and what might be done in order to find out?
[answer]
10. A nationwide television polling agency randomly selects 600 people, of whom 100 watched a particular TV show. Calculate and interpret a 90% confidence interval for the proportion of the population who watched the program.
[answer]
11.
In a workforce survey of a sample of 100 participants 42 were women.
Obtain a 90% CI for the overall (population) proportion [answer]
12.
A political opinion poll was repeated at 6 monthly intervals. It asked if
respondents thought the State premier was doing a good job.
The results were:
Would you conclude that support for the premier had increased?
[answer]
13.
At the last census, 20% of the people in a town were less than 16 years
of age, 20% were aged 16 to 30, 25% were 31 to 45, 15% were aged 46 to
60 and 20% were over 60. The planning department wants to determine if
the age structure of the town has changed since the last census. A
random sample of 200 residents of the town yield the following data:
Test the hypothesis that the age structure of the town has not
changed since the last census. Use a 1% level of significance.
(a) Find the expected frequencies if the age structure has not changed.
[answer]
14.
Suppose that a national trade association has proposed Sydney and Melbourne
as sites for the next national convention. A random sample of 150 delegates
is polled to determine which site is favoured. Using a significance level
of .05 test whether their choice of site is independent of age.
[answer]
15.
Consider the Minitab output below. It shows a linear regression analysis
of biochemical reaction rates on sunlight intensity, and a scatterplot of
the residuals.
(a) Is the regression statistically significant at the 5% level? Give a rea
son to support your answer.
[answer]
Date Number asked 'Yes' responses
March 1990 647 352
September 1990 721 423
(Calculate a 95% CI for the true difference in the population
proportions responding "yes".)
Age (in years) <16 16-30 31-45 46-60 60+
Observed frequency 30 31 37 50 52
(b) Calculate the value of the chi-square statistic.
(c) Test the hypothesis.
Site favoured Age (in years)
0 - 34 35 - 49 50 and over
Sydney 32 63 15
Melbourne 8 22 10
MTB > regress c2 1 c1 residuals in c3
The regression equation is
rate = 48.8 + 3.70 light
Predictor Coef Stdev t-ratio p
Constant 48.800 9.041 5.40 0.000
light 3.701 1.928 1.92 0.063
s = 12.46 R-sq = 9.8% R-sq(adj) = 7.1%
Analysis of Variance
SOURCE DF SS MS F p
Regression 1 571.8 571.8 3.68 0.063
Error 34 5276.5 155.2
Total 35 5848.3
MTB > name c3='Resid'
MTB > plot c3 c1
Resid -
-
- *
1.5+
- * 2 * *
- * * * *
- * * * *
- * *
0.0+ * * * * *
- * *
- * * 2 *
- * *
- **
-1.5+ *
- *
- * *
-
----+---------+---------+---------+---------+---------+--light
2.40 3.20 4.00 4.80 5.60 6.40
(b) What is the correlation between the two variables in this sample?
(c) Calculate a 95% confidence interval for the regression slope (there
are 36 observations in the data set).
(d) Considering the plot of residuals, is this simple linear regression model
a good model for these data? Give your reason.
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