What is the appropriate critical value for each

| March 14, 2016

Question
Practice Part 3

1.

What is the appropriate critical value for each of the following confidence levels and sample sizes? (Rem
in regard to confidence level this implies two-tails)
(a) Critical z-value for an 98% confidence level for sample of size n= 43:

(b) Critical t-value for a 95% confidence level for sample of size n =27:

2

Suppose that the population standard deviation is not known. Under what condition, you can use t-distribu
the inferences about the population mean?

3.

Apple iPad engineers would like to know the mean time for movie downloads. They calculated the downlo
for a specific movie by 12 randomly selected iPads, and the data is shown to the right. Assume all downlo
normally distributed
(a) Determine the mean and standard deviation of this sample data.

(b) Determine the expected margin of error amount in using this sample result to estimate the mean downloa
this same movie of all Apple iPads based upon a 90% desired level of confidence.

(c) Determine the 95% confidence interval for the mean download time all iPads.

(d)

State your final confidence interval result in a sentence that interprets the result within the context of the s

4.

Answer the following:
(a) What is the meaning of the term “null hypothesis” in statistics.

(b) How do you know when to perform a “left-tailed” test in a hypothesis-testing situation versus a “right-tailed
tailed” test?

In multiple choice problems 5 and 6, select the best answer.
5.

A statistical hypothesis test is used to test a claim. You get 1.65 as the test statistic from the collected sa
critical value in a right-tailed test. Which of the following is the correct decision statement for the test?
A.
Fail to reject the null hypothesis
B.
Claim the null hypothesis is true
C.
Reject the null hypothesis
D.
Claim the alternative hypothesis is false

6.

A statistical hypothesis test is used to test a claim. You get a P-value of 0.023 on a test with a significanc
following is the correct decision statement for the test?
A.
Fail to reject the null hypothesis
B.
Claim the null hypothesis is true
C.
Reject the null hypothesis
D.
Claim the alternative hypothesis is false

7.

8.

The posted speed limit on Interstate 30 near New Mexico is 75 miles per hour, but it is claimed that the m
actual speeds of vehicles is greater than 75 miles per hour. Describe the Type II error you could make if y
this claim through a formal hypothesis test on collected data.

The posted speed limit on Interstate 30 near New Mexico is 75 miles per hour, but it is claimed that the m
actual speeds of vehicles is greater than 75 miles per hour. To test this claim, the speeds of 42 randomly
vehicles were taken and then reported to the right.

(a) Give the null and alternative hypotheses for this situation in mathematical notation.

(b) Based upon a 3% level of significance, determine the critical value(s) associated with this hypothesis test

(c) Determine the sample’s test statistic.

(d) State a final conclusion regarding the results of the hypothesis test. Make sure your statement is tied to t
of the problem (speed of vehicles on I-30 near New Mexico).

9.

A report by the NCAA states that 85% of fans want a larger March Madness Tournament. A local educatio
believes that ASU college students also agree with this, so he randomly selects 200 ASU students and fin
178 want a larger tournament. Follow the steps below to conduct a hypothesis test to determine, at the 5%
significance level, if the percentage of students wanting a larger tournament is more than 85%.

(a) List the null and alternative hypotheses for this test.

(b) Determine the value of the sample’s test statistic.

(c) Determine the critical value(s).

(d) Detemine the P-value.

(e) Write a final interpretive sentence tied to the context for the hypothesis test results.

10.

Self-reported heights and measured heights of twelve males aged 12 – 16 are shown in the table to the ri
5% significance level, is there sufficient evidence to support the claim that there is a difference between t
average reported heights and the measured heights of males aged 12 -16? All measurements are in inch
Hypothesis testing method work must be shown for credit on this problem.

11.

At the right, give an example of a paired data set (with at least 5 pairs) that demonstrates a strong (but no
positive linear correlation.

12.

Give a real life example of two variables that are likely to be negatively correlated. Specifically explain wh
believe they are negatively correlated.

13.

Suppose some researchers determine that there is a significant strong positive correlation between a stud
and the final exam grade in Statsitics. From this correlation, can we determine that a student’s GPA is the
a high final exam grade in statistics? Explain your answer.

Use the following situation to answer questions 14 to 18 below:

A criminal laboratory must sometimes estimate a person’s height from partial skeletal remains. A random
eight adult male x-rays gave the following information, where x = length of femur (the thigh bone) in inche
body height in inches. This information will be used to determine a possible relationship between femur le
height.

A criminal laboratory must sometimes estimate a person’s height from partial skeletal remains. A random
eight adult male x-rays gave the following information, where x = length of femur (the thigh bone) in inche
body height in inches. This information will be used to determine a possible relationship between femur le
height.

14.

15.

Produce a scatterplot of this paired data at the right.

Which of the following best describes the correlation that is demonstrated by the scatterplot (C
one best answer.)
A. No Correlation
B. Strong Positive Correlation
C. Strong Negative Correlation
D. Correlation, but not linear

16.

Determine the sample’s correlation coefficient r and the coefficient of determination r2. Then e
clearly whether or not we should conclude that the correlation in these two variables is statisti
significant.

17.

Give the equation of the line-of-best-fit (trend line), the slope of this line, and explain what the
means in the context of this problem.

18.

What should one predict the height of an adult male to be if femur length is 19.5 inches?

nd sample sizes? (Remember that

on, you can use t-distribution to do

ey calculated the download time
right. Assume all download time is

mate the mean download time for
e.

within the context of the situation.

Download time of Apple iPads
24
28
23
26
23
25
24
25

27
26
22
24

tion versus a “right-tailed” or “two-

tic from the collected sample and a 1.85 as your
atement for the test?

a test with a significance level of 0.05. Which of the

ut it is claimed that the mean of the
error you could make if you test

ut it is claimed that the mean of the
speeds of 42 randomly selected

n.

Speed of Randomly Selected Vehicles on I-30
73
77
74
82
68
78
68
72
74
79
74
79
81
76
75
81
75
66
79
72
84
79
83
75

77
77
76
69
69
71

with this hypothesis test.

our statement is tied to the context

nament. A local educational expert
200 ASU students and finds that
st to determine, at the 5%
ore than 85%.

ts.

own in the table to the right. At the
s a difference between the
easurements are in inches. Note:

nstrates a strong (but not perfect)

Reported Height
69
71
64
71
72
61
65
67
58
65
66
70

Measured
Height
67.9
69.9
64.9
68.3
70.3
60.6
64.5
67.0
55.6
64.2
65.0
70.8

x

y

x
17.5

y
72

. Specifically explain why you

orrelation between a student’s GPA
at a student’s GPA is the cause of

letal remains. A random sample of
(the thigh bone) in inches and y =
onship between femur length and

ated by the scatterplot (Choose the

determination r2. Then explain
e two variables is statistically

e, and explain what the slope

gth is 19.5 inches?

20
21
19
15.5
18.5
22
16
18

82
83
81
63
78
85
66
73

82
76
75
76
78
76

73
68
79
80
85
78

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