Elementary Statistics (STA2023)
Homework 8 - 10

8.1.0
 
Most adults would not......mean less than 50 % do not erase all of their personal information.
 
Claim: Most adults would not erase all of their personal information online if they could. A software firm survey of 466
randomly selected adults showed that 44% of them would erase all of their personal information online if they could.
Complete parts​ (a) and​ (b) below.
Express the original claim in symbolic form. Let the parameter represent the adults that would erase their personal information.
 
P < 0.50
​Type an integer or a decimal. Do not​ round.)
 
^H0: P = 0.50
^H1: P < 0.50
 
The claim involves a population proportion.
 
8.1.17
 
The test statistic of z = 0.99 is obtained when testing the claim that p > 0.8
Identify the hypothesis test as being​ two-tailed, left-tailed, or​ right-tailed.
Find the​ P-value.
Using a significance level of a = 0.10​ should we reject Upper ^H0   or should we fail to reject Upper ^H0 ​?
 
This is a right-tailed test.
 a = 0.05
 
If ​P-value ≤ a reject a
If ​P-value > than a fail to reject
 
This is a right-tailed test
 
P-value = 0.176
a = .01
Fail to reject H0 There is not sufficient evidence to support the claim that p > 0.8
 
P-value = 0.008
a = .05
Reject H0. There is sufficient evidence to support the claim that p > 0.5
 
P-value = 0.161
a = .01
 
Fail to reject H0 There is not sufficient evidence to support the claim that p > 0.4
Reject H0. There is not sufficient evidence to support the claim that p > 0.9
Reject H0. There is sufficient evidence to support the claim that p > 0.9
Fail to reject H0 There is not sufficient evidence to support the claim that p > 0.9
Fail to reject H0. There is sufficient evidence to support the claim that p > 0.9.
 

 
8.1.19
 
The test statistic of z = 2.43 is obtained when testing the claim that p ≠ 0.675.
a. Identify the hypothesis test as being​ two-tailed, left-tailed, or​ right-tailed.
b. Find the​ P-value. c. Using a significance level of a = 0.05​, should we reject Upper ^H0   or should we fail to reject Upper ^H0 ​?
 
This is a two-tailed test
 
Since the alternative hypothesis is H 1 ​:  p ≠ 0.474​, this is a two ​-tailed test.
 
a = 0.05
 
If ​P-value ≤ “a” reject H0, If ​P-value > than “a” fail to reject H0
 
P-value = 0.015 ​
A = .05
Reject H0. There is sufficient evidence to support the claim that ≠ 0.675
 
P-value = 0.121
A = .10
Fail to Reject H0. There is not sufficient evidence to support the claim that ≠ 0.182
 
P-value = 0.026
A = .01
 
Fail to Reject H0. There is not sufficient evidence to support the claim that ≠ 0.209
Fail to Reject H0. There is not sufficient evidence to support the claim that ≠ 0.838
Reject H0. There is sufficient evidence to support the claim that ≠ 0.149
 

 
8.1.22
 
The test statistic of z = -2.38 is obtained when testing the claim that p < 0.37 a. Using a significance level of a = 0.05
find the critical​ value(s). b. Should we reject ^H0   or should we fail to reject Upper ^H0 ​?
 
If test statistic is in the critical​ region, reject H0
If test statistic is not in the critical​ region, fail to reject H0
 
test statistic of z = -2.38, a = .05 p < .37
The critical​ value(s) is/are = -1.65
a = .05
Reject H0. There is sufficient evidence to support the claim that p < 0.37
 
The test statistic of z = -2.38, a = .05 p < 27
The critical​ value(s) is/are = -1.65
Reject H0. There is sufficient evidence to support the claim that p < 0.37
 
The test statistic of z = -1.63, a = .01 p < 45
The critical​ value(s) is/are = -2.33
 
Fail to reject   H0.  There is not sufficient evidence to support the claim that p < 0.45

8.1.24
 
The test statistic of z = -2.68 is obtained when testing the claim that p = 2/3.
Using a significance level of a = 0.10 ​, find the critical​ value(s).
Should we reject Upper ^H0   or should we fail to reject Upper ^H0 ​?
 
The critical​ value(s) is/are z = -1.65, 1.65
​(Round to two decimal places as needed. Use a comma to separate answers as​ needed.)
 
https://statscalculator.com/zcriticalvaluecalculator

Enter 0.10
 
Choose the correct conclusion below.
 
If test statistic is in the critical​ region, reject ^H0
If test statistic is not in the critical​ region, fail to reject ^H0
 
Reject Upper ^H0 There is sufficient evidence to warrant rejection of the claim that p = 2/3
Fail to reject ^H0 There is sufficient evidence to warrant rejection of the claim that p = 2/3
Fail to reject ^H0 There is not sufficient evidence to warrant rejection of the claim that p = 2/3
Reject ^H0 There is not sufficient evidence to warrant rejection of the claim that p = 2/3.
 
Reject Upper ^H0 There is sufficient evidence to warrant rejection of the claim that p = 2/3
Fail to reject ^H0 There is sufficient evidence to warrant rejection of the claim that p = 2/3
Fail to reject ^H0 There is not sufficient evidence to warrant rejection of the claim that p = 2/3
Reject ^H0 There is not sufficient evidence to warrant rejection of the claim that p = 2/3.
 
Assume a significance level of alpha equals 0.05 and use the given information to complete parts​ (a) and​ (b) below.
Original​ claim: Less than 53​% of adults would erase all of their personal information online if they could.
The hypothesis test results in a​ P-value of 0.2916
 
Fail to reject ^H0 because the​ P-value is greater than a
 
Without using technical​ terms, state a final conclusion that addresses the original claim.
Which of the following is the correct​ conclusion?
 
There is not sufficient evidence to support the claim that the percentage of adults that would erase all of their personal information online, if they could is less than 53 ​%.

 
Assume a significance level of alpha equals 0.05 and use the given information to complete parts​ (a) and​ (b) below.
Original​ claim: Less than 56​% of adults would erase all of their personal information online if they could. The hypothesis test results in a​ P-value of 0.1517
 
Fail to reject ^H0 because the​ P-value is greater than a
 
Without using technical​ terms, state a final conclusion that addresses the original claim.
Which of the following is the correct​ conclusion?
 
There is not sufficient evidence to support the claim that the percentage of adults that would erase all of
their personal information online, if they could is less than 56%.
 
A. Fail to reject ^H0 because the​ P-value is less than or equal to a
B. Fail to reject ^H0 because the​ P-value is greater than a
C. Reject ^H0 because the​ P-value is less than or equal to a
D. Reject ^H0 because the​ P-value is greater than a
 
A. There is sufficient evidence to support the claim that the percentage of adults that would erase all of their personal information
online if they could is less than 53%.
B. The percentage of adults that would erase all of their personal information online if they could is more than or equal to 53 ​%.
C. The percentage of adults that would erase all of their personal information online if they could is less than 53 ​%.
D. There is not sufficient evidence to support the claim that the percentage of adults that would erase all of their personal information online if they could is less than 53 %.
 

 
Assume a significance level of a = 0.01 and use the given information to complete parts​ (a) and​ (b) below.
Original​ claim: The mean pulse rate​ (in beats per​ minute) of a certain group of adult males is 73 bpm.
The hypothesis test results in a​ P-value of 0.0709. a. State a conclusion about the null hypothesis.​
(Reject Upper H 0 or fail to reject Upper H 0 ​.)  Choose the correct answer below.
 
D. Fail to reject ^H0 because the P-value is greater than a
 
Without using technical​ terms, state a final conclusion that addresses the original claim. Which of the following is the correct​ conclusion?
 
C. There is not sufficient evidence to warrant rejection of the claim that the mean pulse rate​ (in beats per​ minute) of the group of adult males is 73   bpm.
 

 
Assume a significance level of a = 0.01 and use the given information to complete parts​ (a) and​ (b) below. 
Original​ claim: The mean pulse rate​ (in beats per​ minute) of a certain group of adult males is 70 bpm.
The hypothesis test results in a​ P-value of 0.0659. a. State a conclusion about the null hypothesis.​
(Reject Upper H 0 or fail to reject Upper H 0 ​.)
Choose the correct answer below.
 
Fail to reject ^H0 because the P-value is greater than a
 
Without using technical​ terms, state a final conclusion that addresses the original claim.
Which of the following is the correct​ conclusion?
 
There is not sufficient evidence to warrant rejection of the claim that the mean pulse rate​
(in beats per​ minute) of the group of adult males is 70 bpm.
 
A. Reject ^H0 because the P-value is greater than a
B. Fail to reject ^H0 because the P-value is less than or equal to a
C. Reject ^H0 because the P-value is less than or equal to a
D. Fail to reject ^H0 because the P-value is greater than a
 
A. There is sufficient evidence to warrant rejection of the claim that the mean pulse rate​ (in beats per​ minute)
of the group of adult males is 73   bpm.
B. The mean pulse rate​ (in beats per​ minute) of the group of adult males is 73   bpm.
C. There is not sufficient evidence to warrant rejection of the claim that the mean pulse rate​ (in beats per​ minute)
of the group of adult males is 73   bpm.
D. The mean pulse rate​ (in beats per​ minute) of the group of adult males is not 73   bpm
 

---

A certain drug is used to treat asthma. In a clinical trial of the​ drug, 27 of 257 treated subjects experienced headaches​
(based on data from the​ manufacturer). The accompanying calculator display shows results from a test of the claim that
less than 9​% of treated subjects experienced headaches. Use the normal distribution as an approximation to the binomial
distribution and assume a 0.05 significance level to complete parts​ (a) through​ (e) below.
 
a. Is the test​ two-tailed, left-tailed, or​ right-tailed? ​
Left-tailed test
 
What is the test​ statistic? z = 0.84
​(Round to two decimal places as​ needed.)
 
What is the​ P-value?
P-value = 0.8005

p = p-value
 

TI84 Plus Instructions:
STAT     TESTS     PropZTest
P⁰: 0.09
x: 27
n: 257
Calculate, Then Enter
 
z = 0.843533729
p = 0.8005349949
p(hat) = 0.1050583658
n = 257
 
Decide whether to reject the null hypothesis. Choose the correct answer below.
Fail to reject   the null hypothesis because the​ P-value is > the significance​ level, a
 
What is the final​ conclusion?
There is not sufficient evidence to support the claim that less than 9% of treated subjects experienced headaches.
 
Consider the significance​ level, α​, and the​ P-value to decide if the null​ hypothesis, H0​, should be rejected.
If the​ P-value is less than or equal to the significance​ level, reject the null hypothesis.
If the​ P-value is greater than the significance​ level, fail to reject the null hypothesis.
 

 
8.2.10T
Consider a drug that is used to help prevent blood clots in certain patients. In clinical​ trials, among 6187 patients
treated with this​ drug, 161   developed the adverse reaction of nausea. Use a 0.05   significance level to test the
claim that 3​% of users develop nausea. Does nausea appear to be a problematic adverse​ reaction?
 
Identify the null and alternative hypotheses for this test. Choose the correct answer below.
 
H₀: p = .03
H₀: p ≠ .03

Identify the test statistic for this hypothesis test.
The test statistic for this hypothesis test is -1.83
​(Round to two decimal places as​ needed.)
 
TI84 Plus Instructions:
STAT / TEST / stats
PropZTest: P:  .03 / x: 161 / n: 6167 / ≠p
 
The​ P-value for this hypothesis test is 0.067
(Round to three decimal places as​ needed.)
 
TI84 Plus Instructions:
2^nd    VARS      Normalcdf
-9999
-1.83
0
1
= .0336249107

0.0336249107 x 2 = 0.0672498214
 
Identify the conclusion for this hypothesis test.
 
A. Fail to reject   Upper H0 .  There is   sufficient evidence to warrant rejection of the claim that 3 ​% of users develop nausea.
B. Reject   Upper H 0.  There is  sufficient evidence to warrant rejection of the claim that 3 % of users develop nausea.
C. Fail to reject   Upper H0 .  There is not   sufficient evidence to warrant rejection of the claim that 3 ​% of users develop nausea. Your answer is correct.
D. Reject   Upper H0 .  There is not   sufficient evidence to warrant rejection of the claim that 3 ​%  of users develop nausea.
 
Does nausea appear to be a problematic adverse​ reaction?
Since the rate of nausea appears to be relatively low, it is not a problematic adverse reaction.
 

 
Suppose that in a random selection of 100 colored​ candies, 21% of them are blue. The candy company claims that the percentage of blue candies is equal to 26%. Use a 0.01   significance level to test that claim.
 
Identify the null and alternative hypotheses for this test. Choose the correct answer below.
 
^H0​: p = 0.26
^H0​: p ≠0.26
 
Null hypothesis: H0: p = 0.26
Alternative hypothesis: H0: 0≠ 0.26
 
Identify the test statistic for this hypothesis test.
The test statistic for this hypothesis test is -1.14
​(Round to two decimal places as​ needed.)
 
TI84 Plus Instructions:
STAT      TESTS      PropZTest
P: = 0.26
x = 21
n = 100
≠p
z = -1.139901891
 
Identify the​ P-value for this hypothesis test.

The​ P-value for this hypothesis test is 0.254   (Round to three decimal places as​ needed.)
 
TI84 Plus Instructions:
2^nd     VARS     Normalcdf:
-9999
-1.14
0
1
= 0.12714132013 x 2

0.12714132013 x 2 = 0.2542

https://www.graphpad.com/quickcalcs/pvalue1.cfm
 
Identify the conclusion for this hypothesis test.
 
A. Fail to reject Upper ^H0.
There is not sufficient evidence to warrant rejection of the claim that the percentage of blue candies is equal to 26 %
B. Reject Upper ^H0. There is not sufficient evidence to warrant rejection of the claim that the percentage of blue candies is equal to 26​%
C. Reject Upper ^H0. There is sufficient evidence to warrant rejection of the claim that the percentage of blue candies is equal to 26%
D. Fail to reject Upper ^H0. There is sufficient evidence to warrant rejection of the claim that the percentage of blue candies is equal to 26 %