Final Exam Review

1
Final Exam Review
2
Keller 10.13

• A random sample of 50 young adult men (20-30
  years old) was sampled. Each person was asked how
  many minutes of sports they watch on television
  daily. The sample mean was found to be x-bar
  64. Suppose that ? 20. Test to determine at the
  5 significance level whether there is enough
  statistical evidence to infer that the mean
  amount of television watched by all young men is
  greater than 60 minutes.

3
Keller 10.13 - Solution
1.41, p-value P (z gt 1.41) .0793

Conclusion Do not reject the null hypothesis.
There is not enough evidence to infer that the
mean amount of television watched by all young
adult men is greater than 60 minutes.
4
Keller 10.14

• Repeat Keller 10.13 with n 25

1.00, p-value P(z gt 1.00) .1587
Conclusion Do not reject the null hypothesis.
There is not enough evidence to infer that the
mean amount of television watched by all young
adult men is greater than 60 minutes.
5
Keller 10.15

• Repeat Keller 10.13 with n 100

2.00, p-value P(z gt 2.00) .0228
Conclusion Reject the null hypothesis. There
is enough evidence to infer that the mean amount
of television watched by all young adult men is
greater than 60 minutes.
6
Keller 10.16

• Repeat Keller 10.13 with ? 10

2.83, p-value P(z gt 2.83) .0023
Conclusion Reject the null hypothesis. There
is enough evidence to infer that the mean amount
of television watched by all young adult men is
greater than 60 minutes.
7
Keller 10.17

• Repeat Keller 10.13 with ? 40

.71, p-value P(z gt .71) .2389
Conclusion Do not reject the null hypothesis.
There is not enough evidence to infer that the
mean amount of television watched by all young
adult men is greater than 60 minutes.
8
Keller 10.18

• Repeat Keller 10.13 with x-bar 62

.71, p-value P(z gt .71) .2389
Conclusion Do not reject the null hypothesis.
There is not enough evidence to infer that the
mean amount of television watched by all young
adult men is greater than 60 minutes.
9
Keller 10.19

• Repeat Keller 10.13 with x-bar 68

2.83, p-value P(z gt 2.83) .0023
Conclusion Reject the null hypothesis. There
is enough evidence to infer that the mean amount
of television watched by all young adult men is
greater than 60 minutes.
10
Keller 11.28

• The following are a random sample of pipe lengths
  cut for a production facility.
• Estimate the population mean with 95 confidence
• Test to determine if we can infer at 10
  significance level that the population mean is
  greater than 20
• What is the required condition of the techniques
  used in part a) and b). Use a graphical technique
  to check to see if that required condition is
  satisfied

11
Keller 11.28

• a) LCL 21.19, UCL 24.01

Rejection region
b) Conclusion Reject the null hypothesis. There
is enough evidence to infer that the population
mean is greater than 20.
12
Keller 11.28
The population is required to be normal. The
condition appears not to be satisfied.
13
Keller 11.41
The following data were drawn from a normal
population 85, 59, 66, 81, 35, 57, 55, 63, 66 At
5 significance, test to determine if there is
enough evidence to conclude that the population
variance is greater than 100.
p-value (Excel) .0275 Rejection region
Conclusion Reject the null hypothesis. There is
enough evidence to infer that the variance is
greater than 100.
14
Keller 11.68
In a television commercial, the manufacturer of a
toothpaste claims that more than four out of five
dentist surveyed recommend the ingredients in his
product. To test that claim, a consumer-protection
group randomly samples 400 dentists and asks
each one whether he or she would recommend
toothpaste that contained the ingredients. The
responses are 1 No and 2 Yes. The responses
are found in file XR11-68. At the 5 significance
level, can the consumer group infer that the
claim is true?
15
Keller 11.68
p-value P(z gt 1.13) .1292
Rejection region
Conclusion Do not reject the null hypothesis.
There is not enough evidence to infer that the
claim is true.
16
Keller 12.11
After drawing random samples from two normal
populations, a statistician produced the
following statistics. a) Can we infer at 10
significance level that µ1 is less than µ2? b)
Estimate with 95 confidence the difference in
population means
17
Keller 12.11
Conclusion Reject the null hypothesis. There is
enough evidence to infer that is less than .
18
Keller 12.11
or LCL -180, UCL 22
19
Keller 12.12
Repeat with the following new sample standard
deviations
Conclusion Do not reject the null hypothesis.
There is not enough evidence to infer that is
less than .
20
Keller 12.12
LCL -276.41, UCL 118.41
21
Keller 12.13
Discuss the effect of increasing the sample
standard deviations.
The t-statistic decreases and the interval
narrows.
22
Keller 12.14
Repeat with the following new sample sizes
Conclusion Reject the null hypothesis. There is
enough evidence to infer that is less than .
23
Keller 12.14
or LCL -147.09, UCL -10.91
24
Keller 12.15
Describe what happens when the sample size
increases.
The t-statistic becomes more negative and the
interval narrows.
25
Keller 12.16
Repeat with the following new sample mean
Conclusion Reject the null hypothesis. There is
enough evidence to infer that is less than .
26
Keller 12.16
or LCL -214, UCL -12
27
Keller 12.17
Repeat with the following new sample mean
Conclusion Do not reject the null hypothesis.
There is not enough evidence to infer that is
less than .
28
Keller 12.17
or LCL -164, UCL 38
29
Keller 12.18
Discuss the effect of increasing and decreasing
the sample mean
The farther x-bar1 is from x-bar2 the more
negative the t-statistic. The width of the
interval is not affected by increasing or
decreasing x-bar1
30
Keller 12.50
Given the data below, test the following
hypotheses Sample 1 7, 4, 9, 12, 8, 6, 9,
14 Sample 2 10, 7, 13, 18, 4, 8, 21, 20, 5, 8
31
Keller 12.50
Given the data below, test the following
hypotheses Sample 1 7, 4, 9, 12, 8, 6, 9,
14 Sample 2 10, 7, 13, 18, 4, 8, 21, 20, 5, 8
Conclusion Reject the null hypothesis. There is
enough evidence to infer that the population
variances differ.
32
Keller 12.70
Hismanal is a cold and allergy product that
claims to be the first, once-a-day nondrowsy
alergy medicine. The nondrowsy part of the claim
is based on a clinical experiment in which 1604
patients were given Hismanal and 1109 patients
were given a placebo 7.1 of the first group and
6.4 of the second group reported drowsiness. Do
these results allow us to infer at the 5
significance level that Hismanals claim is false?
33
Keller 12.70
p-value (Excel) .2384 Rejection region
Conclusion Do not reject the null hypothesis.
There is not enough evidence to infer that
Hismanal's claim is false.