Download Statistics for Everyday Life – MORE Practice

Statistics for Everyday Life – MORE Practice
1.
A random sample of 6 people was put on a strict exercise program. Your goal is to use the following output to see if the
program helps people lose weight.
Paired T-Test and CI: Before, After
N
Mean
StDev SE Mean
Before
6 215.500
21.436
8.751
After
6 210.500
17.306
7.065
Difference 6 5.00000 5.47723 2.23607
T-Test of mean difference = 0 (vs > 0): T-Value = 2.24
a)
b)
c)
d)
P-Value = 0.038
The average difference in weight is __[5]__
Give the hypothesis:
Ho: __[μd = 0 no program effect]__
Ha: __[μd > 0 program effective]__
Give the value of the test statistic = __[2.24]__
Give the decision and conclusion if α = 0.05.
[Reject Ho since P-value = 0.038 is small (less than 0.05) -- conclude program helps people lose weight.]
2.
A stats professor wants to see if there is a difference in the average exam scores between day and evening basic stats
students. A sample of 28 day students and 25 evening students is taken. Which analysis would be appropriate? __[A]__
A) 2-Sample t-test
B) Paired t-test
C) Chi-Square test
D) Correlation Analysis
3.
A junior high school teacher wants to see if there is a relationship between hours spent watching TV per week and
achievement test scores. Which analysis would be appropriate? __[D]__
A) 2-Sample t-test
B) Paired t-test
C) Chi-Square test
D) Correlation Analysis
4.
Last semester the blood pressure levels of 20 Statistics for Everyday Life students were taken just prior to the final, and
then again just after they finished. The data were summarized and a statistical test was done to see if, on average, blood
pressure levels increase for all students taking the final. In this case, the appropriate statistical procedure is the __[B]__
A) 2-Sample t-test
B) Paired t-test
C) Chi-Square test
D) Correlation Analysis
5.
A researcher wants to see if wearing a pair of prescription glasses depend on the gender of the person.
Here, the researcher will do which of the following analysis? __[C]__
A) 2-Sample t-test
B) Paired t-test
C) Chi-Square test
D) Correlation Analysis
6.
For their lab project, one group wants to find out which brand of toilet paper is most popular among UA students.
What kind of graph would be most appropriate in displaying their findings? __[D]__
A) Histogram
B) Stem-and-Leaf
C) Side-by-Side Box Plot
D) Pie-Chart
7.
For their lab project, another group wants to compare heights, in inches, of male and female basketball players at UA.
What kind of graph would be most appropriate in displaying their findings? __[C]__
A) Histogram
B) Pie-Chart
C) Side-by-Side Box Plot
D) Bar Graph
8.
For a stats exam, 2 forms of the test were used. One was on white paper(W) and the other on yellow(Y). However, the
questions on each form were exactly the same, and in the same order. The was done to see if there is a significant difference
between the two types of the exam, in other words, was the color of the test determine the score on the exam. The following
is the MINITAB output. Answer questions that follow.
Two-Sample T-Test and CI: Test 1, Color
Color
N
Mean
StDev
SE Mean
W
46
81.7
12.8
1.9
Y
47
75.8
15.1
2.2
Difference = mu (W) - mu (Y)
Estimate for difference: 5.82
T-Test of difference = 0 (vs not =): T-Value = 2.00 P-Value = 0.048 DF = 89
a) Give the hypothesis in symbols: Ho: __[μwhite – μyellow = 0]__
Ha: __[μwhite – μyellow not equal 0]__
b) Which group had a larger mean score? (W or Y) __[W]__; larger standard deviation? (W or Y) __[Y]__
c) What do you conclude 5% sig level about effect of color on the score? [Reject Ho … Yes Color Effect Exists On Scores]
9.
The median of a data set is also known as the __[2nd]__ quartile.
10. What shape would you predict for a distribution of test scores with a mean of 68 and median of 81? __[skewed left]__
11. A __[C]__ is a sample selected so that every member of the population had an equal chance of being selected and each
selection is made independently. A) Stratified sample B) Systematic sample C) Random sample D) Cluster sample
12. Match the symbol with the appropriate definition.
p̂ __[B]__
 __[A]__
A) population mean
n __[F]__
B) sample proportion
x
s __[C]__
p __[G]__
C) sample standard deviation
D) population standard deviation
__[E]__
 __[D}__
E) sample mean
F) sample size
G) population proportion
13. Failing to reject Ho when Ho is false is __[B]__
A) a type I error.
B) a type II error.
C) a type III error.
D) a correct decision.
14. Other things being equal, increasing the sample size causes the width of the confidence interval to: __[B]__
A) increase.
B) decrease.
C) stay the same.
15. Other things being equal, decreasing the confidence level causes the width of the confidence interval to: __[B]__
A) increase.
B) decrease.
C) stay the same.
16. Which one of the following random variables is closest to a binomial distribution? __[A]__
A. The number of orders out of the next 10 that include fries.
B. The net weight of a randomly selected small order of fries.
C. The fat content of a randomly selected order of fries
D. The amount of time that a randomly selected customer has to wait in line.
17. Two random samples, one of blue-collar workers and a second sample of white-collar workers were taken from a large company.
These workers were asked about their views on a certain company issue. We test to see whether Workers and Opinion are
related at 1% significance level.
Chi-Square Test: Favor, Oppose, Uncertain
Expected counts are printed below observed counts
Blue-Collar
White-Collar
Total
Favor
40
40.00
Oppose
37
40.00
Uncertain
23
20.00
20
20.00
23
20.00
7
10.00
60
60
30
Total
100
50
150
Chi-Sq = 2.025, DF = 2, P-Value = 0.363
a)
Give the null hypothesis:
Ho: __[No Association B/W Worker Status & Opinion]__
b) What is the value of the test statistic? __[2.025]__
c) What do you conclude at 5% significance level? Justify your answer.
[Fail To Reject Ho Since Large P-value = 0.363 – Insufficient Evidence Of Association B/W Worker Status & Opinion]
18. It was reported that, in a sample of 568 adult Americans, only 142 correctly described the Bill of Rights as the first ten
amendments to the U.S. Constitution. Calculate a (two-sided) confidence interval using a 99% confidence level for the
proportion of all U.S. adults that could give a correct description of the Bill of Rights. (6 pts)
Sample Prop. Std. Err.
L. Limit
0.25
0.018168809 0.20320025
U. Limit
0.29679975
19.
An airline's public relations department says that the airline rarely loses passengers'
luggage. It further claims that on those occasions when luggage is lost, 88% is recovered and
delivered to its owner within 24 hours. A consumer group who surveyed a large number of air
travelers found that only 132 out of 165 people who lost luggage on that airline were reunited
with the missing items by the next day. Does this cast doubt on the airline's claim?
Perform the appropriate test at the 0.05 -level.
[Ho: p = 0.88 H1: p < 0.88
[z 
pˆ  p
 pˆ
[ pˆ  132 / 165  0.8  pˆ 
(0.88)(0.12)
0.8  0.88
 0.0253 z 
 3.16
165
0.0253
[p-value = P(Z < -3.16)= 0.0008
[Small p-value (less than 0.05) --- Reject Ho!!!
[This data shows that the actual proportion of passengers with lost luggage are
[reunited with it within 24 hours is less than the 88% claimed by the airline.