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Supplemental Review Questions
1. Complete the following sentences:
1) The main idea of significance tests is: An effect that is highly unlikely to be observed if the claim about
the parameter is true is evidence that ___________________________________
2) If p-value < significance level, we _______________________________________
3) Claim (H0): (I’m a bit concerned that) s/he doesn’t love me. Evidence: S/he organizes a romantic trip
to Europe for us. I find (statistically) from many people’s experience that the probability will be very low
that s/he organizes a romantic trip to Europe for us, if s/he doesn’t love me (that is, H0 is true), which is
good evidence that s/he probably _____ (does or doesn’t?) love me.
2. Is the weight of bags of tortilla chips as advertised?
Bags of a certain brand of tortilla chips claim to have a net weight of 14 ounces. Net weights actually
vary slightly from bag to bag and are normally distributed with mean µ.
1) A representative of a consumer advocate group wishes to see if there is any evidence that the mean net
weight is less than advertised and so intends to test the hypotheses:
H0: __________________ In words:____________________________
Ha:__________________ In words:____________________________
To do this, he selects 16 bags of this brand at random and determines the net weight of each. He finds the
sample mean to be 13.88 and the sample standard deviation to be 0.24 which is assumed to the same as
the population standard deviation.
2) Construct a test statistic. Write down the formula for this test statistic: __________________
3) Calculate the value of this test statistic: __________________________________
4) What is the p-value [Use Table A: Standard Normal probabilities]
________________________________________________
5) Interpret this p-value. ________________________________________________
6) Using a conventional significance level of 5%, what can you conclude?
____________________________________________________________________________
3. Does the water diet work?
The water diet requires one to drink two cups of water every half hour from when one gets up until one
goes to bed, but otherwise allows one to eat whatever one likes. Four adult volunteers agree to test the
diet. They are weighed prior to beginning the diet and after six weeks on the diet. The weights (in
pounds) are
Person 1 2 3 4
Weight before the diet 180 125 240 150
Weight after six weeks 170 130 215 152
For the population of all adults, assume that the weight loss after six weeks on the diet (weight before
beginning the diet minus weight after six weeks on the diet) is normally distributed with mean µ.
1) To determine if the diet leads to weight loss, we test the hypotheses:
H0: __________________ In words:____________________________
Ha:__________________ In words:____________________________
2) What is the value of the observed sample mean x-bar? ______________________________
4. Balance a checkbook
In a discussion of the education level of the American workforce, someone says, “The average young
person can’t even balance a checkbook.” The National Assessment of Educational Progress says that a
score of 275 or higher on its quantitative test reflects the skill needed to balance a checkbook. Suppose we
know that NAEP scores have a Normal distribution with σ = 60. The NAEP random sample of 840 young
men had a mean score of = 272, a bit below the checkbook-balancing level. Is this sample result good
evidence that the mean for all young men is less than 275?
1) Write down the null and alternative hypotheses, both in symbols and in words.
2) Write down the test statistic formula and calculate the value of the Test Statistic.
3) What type of test is this? What is the P-value?
4) Suppose the significance level α = 0.10 (or 10%), draw your conclusion.
5. SAT math exams
We suspect that on the average students will score higher on their second attempt at the SAT mathematics
exam than on their first attempt. Suppose we know that the changes in score (second try minus first try)
follow a Normal distribution with standard deviation σ=50. Here are the results for 46 randomly chosen
high school students:
−30 24 47 70 −62 55 −41 −32 128 −11
−43 122 −10 56 32 −30 −28 −19 1 17
57 −14 −58 77 27 −33 51 17 −67 29
94 −11 2 12 −53 −49 49 8 −24 96
120 2 −33 −2 −39 99
Do these data give good evidence that the mean change in the population is greater than zero?
To answer this question, please follow the following four steps:
1) Write down the null and alternative hypotheses, both in symbols and in words.
2) Write down the test statistic formula and calculate the value of the Test Statistic.
3) What type of test is this? What is the P-value?
4) Suppose the significance level α = 0.10 (or 10%), draw your conclusion.
6. Regression
Based on the SPSS results below, answer the questions that follow.
Model Summary
Model R R Square
Adjusted R
Square
Std. Error of the
Estimate
1 .641a
.411 .386 28.41718
a. Predictors: (Constant), state median household income (in
thousands of $s), percent adults that are smokers
Coefficientsa
Model
Unstandardized Coefficients
Standardized
Coefficients
B Std. Error Beta t Sig.
1 (Constant) 175.617 58.394 3.007 .004
percent adults that are
smokers
5.385 1.552 .465 3.469 .001
state median household
income (in thousands of $s)
-1.350 .722 -.251 -1.868 .068
a. Dependent Variable: heart disease death rate (# of deaths from heart disease for every 1,000,000 people in
state)
1) Using the names of the variables (not just X and Y) and the results provided by SPSS,
write down the regression equation that was estimated here.
2) Provide interpretations of the estimated slopes, the estimated constant term, and Rsquared.
3) Use the regression model to predict the heart disease death rate for a state with 20 percent
of adult smokers and state median household income being $52,000. Show all the main
steps.
4) The SPSS output contains results related to the following hypothesis: Ho: A state’s
adults’ smoking rate has no effect on its heart disease death rate, “b=0”. Ha: A state’s
adults’ smoking rate has an effect on its heart disease death rate, “b≠0”.
a. What type of hypothesis test is this?
b. What is the value of the test statistic that SPSS calculated?
c. What is the p-value that SPSS calculated?
d. Using a significance level of 1%, explain what conclusions you can draw.
5) At the significance level of 1%, is the slope for “state median household income”
statistically significantly different from 0? Indicate: yes or no. What about 10% level?
7. Cross Tabulation and Chi-Square Test
Based on the SPSS results below, answer the questions that follow.
gender * education category Crosstabulation
education category
Total
1. lt highschool 2. ged
3. high-school
graduate
4. some
college
5. college and
above
gender 1.male Count 34 8 30 29 33 134
Expected
Count
33.0 5.4 43.8 24.2 27.6 134.0
Residual 1.0 2.6 -13.8 4.8 5.4
2.female Count 45 5 75 29 33 187
Expected
Count
46.0 7.6 61.2 33.8 38.4 187.0
Residual -1.0 -2.6 13.8 -4.8 -5.4
Total Count 79 13 105 58 66 321
Expected
Count
79.0 13.0 105.0 58.0 66.0 321.0
Chi-Square Tests
Value df
Asymp. Sig. (2-
sided)
Pearson Chi-Square 13.116a 4 .011
Likelihood Ratio 13.369 4 .010
Linear-by-Linear Association .773 1 .379
N of Valid Cases 321
a. 0 cells (.0%) have expected count less than 5. The minimum expected
count is 5.43.
1) What are the two categorical variables being analyzed?
2) What is the marginal distribution of the education attainment in the sample? Report in
counts and in percent.
3) What is the conditional distribution of the education attainment among women in the
sample? Report in counts and in percent.
4) Are there any differences in educational attainment between men and women? Explain
briefly based on your calculations in 2) and 3).
5) What is the chi-square value in the SPSS results? Please show all the steps to calculate by
hand the chi-square value.
6) Based on the SPSS results of the chi-square test, what conclusion can you draw at the 5%
significance level?
8. Confidence Interval & Significance Tests
A 95% confidence interval for a population mean is 31.5 ± 3.5.
1) Can you reject the null hypothesis that μ=34 at the 5% significance level? Why? (We assume a twosided alternative.)
2) Can you reject the null hypothesis that μ=36 at the 5% significance level? Why? (We assume a twosided alternative.)
9. Confidence Interval & Significance Test (Two-sample t test)
The results of surveys conducted by the Center for Disease Contro are shown in the table below.
We will focus on the weight of 30-39 years old males in 1960-1962, for questions 1) and 2):
1) What must have been the sample standard deviation for this group?
2) Calculate a 90% confidence interval for the mean weight for this population.
3) Test whether the average weight of 30-39 year old males has increased between 1960-
1962 and 1971-1974, using 1% significance level.

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