07 Jan What is the regression?
Homework 5
1. The claim is that the proportion of peas with yellow pods is equal to 0.25? (or 25%). The sample statistics from one experiment include 400 peas with 115 of them having yellow pods. Find the value of the test statistic.
The value of the test statistic is ____-?(Round to two decimal places as? needed.)
2. Assume that the significance level is alpha equals 0.01. Use the given information to find the? P-value and the critical? value(s).
The test statistic of zequals1.78 is obtained when testing the claim that p greater than 0.4.
Click here to view page 1 of the Normal table. LOADING… Click here to view page 2 of the Normal table. LOADING…
?P-value = _____-?(Round to four decimal places as? needed.)
The critical? value(s) is/are z = _____?(Round to two decimal places as needed. Use a comma to separate answers as? needed.)
3. Assume a significance level of alpha equals 0.05 and use the given information to complete parts? (a) and? (b) below.
Original? claim: The proportion of male golfers is more than 0.8. The hypothesis test results in a? P-value of 0.007.
a. State a conclusion about the null hypothesis.? (Reject Upper H 0 or fail to reject Upper H 0?.) Choose the correct answer below.
A.
Reject Upper H 0 because the? P-value is greater than alpha.
B.
Reject Upper H 0 because the? P-value is less than alpha.
C.
Fail to reject Upper H 0 because the? P-value is greater than alpha.
D.
Fail to reject Upper H 0 because the? P-value is less than alpha.
b. Without using technical? terms, state a final conclusion that addresses the original claim. Which of the following is the correct? conclusion?
A.
There is not sufficient evidence to reject the claim that the proportion of male golfers is??more than 0.8.
B.
There is sufficient evidence to reject the claim that the proportion of male golfers is??more than 0.8.
C.
There is sufficient evidence to support the claim that the proportion of male golfers is more than 0.8.
D.
There is not sufficient evidence to support the claim that the proportion of male golfers is more than 0.8.
4. Identify the type I error and the type II error that correspond to the given hypothesis.
The percentage of adults who retire at age 65 is less than 62 %.
Identify the type I error. Choose the correct answer below.
A.
Fail to reject the null hypothesis that the percentage of adults who retire at age 65 is less than 62 % when the percentage is actually equal to 62 %.
B.
Reject the null hypothesis that the percentage of adults who retire at age 65 is equal to 62 % when that percentage is actually equal to 62 %.
C.
Reject the null hypothesis that the percentage of adults who retire at age 65 is less than 62 % when that percentage is actually less than 62 %.
D.
Fail to reject the null hypothesis that the percentage of adults who retire at age 65 is equal to 62 % when that percentage is actually less than 62 %.
Identify the type II error. Choose the correct answer below.
A.
Fail to reject the null hypothesis that the percentage of adults who retire at age 65 is equal to 62 % when that percentage is actually less than 62 %.
B.
Reject the null hypothesis that the percentage of adults who retire at age 65 is less than 62 % when that percentage is actually less than 62 %.
C.
Fail to reject the null hypothesis that the percentage of adults who retire at age 65 is less than 62 % when the percentage is actually equal to 62 %.
D.
Reject the null hypothesis that the percentage of adults who retire at age 65 is equal to 62 % when the percentage is actually equal to 62 %.
5. A genetic experiment involving peas yielded one sample of offspring consisting of 430 green peas and 156 yellow peas. Use a 0.05 significance level to test the claim that under the same? circumstances, 26?% of offspring peas will be yellow. Identify the null? hypothesis, alternative? hypothesis, test? statistic, P-value, conclusion about the null? hypothesis, and final conclusion that addresses the original claim. Use the? P-value method and the normal distribution as an approximation to the binomial distribution.
What are the null and alternative? hypotheses?
A.
Upper H 0 : p not equals 0.26
Upper H 1 : p equals 0.26
B.
Upper H 0 : p not equals 0.26
Upper H 1 : p greater than 0.26
C.
Upper H 0 : p equals 0.26
Upper H 1 : p greater than 0.26
D.
Upper H 0 : p equals 0.26
Upper H 1 : p less than 0.26
E.
Upper H 0 : p not equals 0.26
Upper H 1 : p less than 0.26
F.
Upper H 0 : p equals 0.26
Upper H 1 : p not equals 0.26.
What is the test? statistic?
Z = _________?(Round to two decimal places as? needed.)
What is the? P-value?
?P-value =__________?(Round to four decimal places as? needed.)
What is the conclusion about the null? hypothesis?
A.
Reject the null hypothesis because the? P-value is less than or equal to the significance? level, alpha.
B.
Fail to reject the null hypothesis because the? P-value is greater than the significance? level, alpha.
C.
Reject the null hypothesis because the? P-value is greater than the significance? level, alpha.
D.
Fail to reject the null hypothesis because the? P-value is less than or equal to the significance? level, alpha.
What is the final? conclusion?
A.
There is sufficient evidence to support the claim that less than 26?% of offspring peas will be yellow.
B.
There is sufficient evidence to warrant rejection of the claim that 26?% of offspring peas will be yellow.
C.
There is not sufficient evidence to support the claim that less than 26?% of offspring peas will be yellow.
D.
There is not sufficient evidence to warrant rejection of the claim that 26?% of offspring peas will be yellow.
6. Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative? hypotheses, test? statistic, P-value, and state the final conclusion that addresses the original claim.
A simple random sample of 25 filtered 100 mm cigarettes is? obtained, and the tar content of each cigarette is measured. The sample has a mean of 19.0 mg and a standard deviation of 3.54 mg. Use a 0.05 significance level to test the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 ?mg, which is the mean for unfiltered king size cigarettes. What do the results? suggest, if? anything, about the effectiveness of the? filters?
What are the? hypotheses?
A.
Upper H 0?: muless than21.1 mg
Upper H 1?: mugreater than or equals21.1 mg
B.
Upper H 0?: muequals21.1 mg
Upper H 1?: mugreater than or equals21.1 mg
C.
Upper H 0?: mugreater than21.1 mg
Upper H 1?: muless than21.1 mg
D.
Upper H 0?: muequals21.1 mg
Upper H 1?: muless than21.1 mg
Identify the test statistic.
T = _______?(Round to three decimal places as? needed.)
Identify the? P-value.
The? P-value is ______?(Round to four decimal places as? needed.)
State the final conclusion that addresses the original claim. Choose the correct answer below.
A.
Reject Upper H 0. There is insufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.
B.
Fail to reject Upper H 0. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.
C.
Reject Upper H 0. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.
D.
Fail to reject Upper H 0. There is insufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.
What do the results? suggest, if? anything, about the effectiveness of the? filters?
A.
The results suggest that the filters increase the tar content.
B.
The results are inconclusive because the sample size is less than 30.
C.
The results suggest that the filtered cigarettes have the same tar content as unfiltered king size cigarettes.
D.
The results suggest that the filters are effective.
E.
The results do not suggest that the filters are effective.
7. The accompanying data table lists measured voltage amounts supplied directly to a? family’s home. The power supply company states that it has a target power supply of 120 volts. Using those home voltage? amounts, test the claim that the mean is 120 volts. Use a 0.05 significance level.
Day
Volts
1
124.5124.5
2
123.9123.9
3
123.9123.9
4
123.7123.7
5
123.4123.4
6
123.3123.3
7
123.3123.3
8
123.6123.6
9
123.5123.5
10
123.9123.9
11
123.5123.5
12
123.7123.7
13
124.3124.3
14
123.7123.7
15
123.9123.9
16
124.0124.0
17
124.2124.2
18
124.1124.1
19
123.8123.8
20
123.8123.8
Day
Volts
21
124.0124.0
22
123.9123.9
23
123.6123.6
24
123.8123.8
25
123.4123.4
26
123.4123.4
27
123.4123.4
28
123.4123.4
29
123.3123.3
30
123.9123.9
31
123.5123.5
32
123.6123.6
33
123.6123.6
34
123.9123.9
35
123.9123.9
36
123.8123.8
37
123.9123.9
38
123.7123.7
39
123.8123.8
40
123.8
What are the null and alternative? hypotheses?
A.
Upper H 0?: muequals120
Upper H 1?: mugreater than120
B.
Upper H 0?: muequals120
Upper H 1?: munot equals120
.C.
Upper H 0?: munot equals120
Upper H 1?: muequals120
D.
Upper H 0?: munot equals120
Upper H 1?: mugreater than120
Calculate the test statistic.
?(Round to three decimal places as? needed.)
What is the range of values for the? P-value?
Choose the correct answer below.
A.
Upper P dash value less than 0.01
B.
0.10 less than Upper P dash value less than 0.20
C.
0.025 less than Upper P dash value less than 0.05
D.
Upper P dash value greater than 0.20
E.
0.01 less than Upper P dash value less than 0.025
F.
0.05 less than Upper P dash value less than 0.10
Identify the critical? value(s).
?(Round to three decimal places as needed. Use a comma to separate answers as? needed.)
State the final conclusion that addresses the original claim.______Upper H 0. There is _____evidence to warrant rejection of the claim that the mean voltage is 120 volts.
8. What is the difference between the following two regression? equations?
ModifyingAbove y with caret equals b 0 plus b 1 x y equals beta 0 plus beta 1 x
Choose the correct answer below.
A.
The first equation is for a? population; the second equation is for sample data.
B.
The first equation is for sample? data; the second equation is for a population.
9. Suppose IQ scores were obtained from randomly selected twins. For 20 such pairs of? people, the linear correlation coefficient is 0.948 and the equation of the regression line is ModifyingAbove y with caret equals negative 13.53 plus 1.12 x?, where x represents the IQ score of the twin born second. ?Also, the 20 x values have a mean of 101.82 and the 20 y values have a mean of 100.05. What is the best predicted IQ of the twin born first?, given that the twin born second has an IQ of 110?? Use a significance level of 0.05.
Critical Values of the Pearson Correlation Coefficient r
?NOTE: To test
H0?:
rho?equals=0
against
H1?:
rho?not equals??0,
reject
H0
if the absolute value of r is greater than the critical value in the table.
n
alpha?equals=0.05
alpha?equals=0.01
4
0.950
0.990
5
0.878
0.959
6
0.811
0.917
7
0.754
0.875
8
0.707
0.834
9
0.666
0.798
10
0.632
0.765
11
0.602
0.735
12
0.576
0.708
13
0.553
0.684
14
0.532
0.661
15
0.514
0.641
16
0.497
0.623
17
0.482
0.606
18
0.468
0.590
19
0.456
0.575
20
0.444
0.561
25
0.396
0.505
30
0.361
0.463
35
0.335
0.430
40
0.312
0.402
45
0.294
0.378
50
0.279
0.361
60
0.254
0.330
70
0.236
0.305
80
0.220
0.286
90
0.207
0.269
100
0.196
0.256
n
alpha?equals=0.05
alpha?equals=0.01
The best predicted IQ of the twin born first is_____.
?(Round to two decimal places as? needed.)
10. The data show the time intervals after an eruption? (to the next? eruption) of a certain geyser. Find the regression? equation, letting the first variable be the independent? (x) variable. Find the best predicted time of the interval after an eruption given that the current eruption has a height of 127 feet. Use a significance level of 0.05.
Height? (ft)
70
73
104
122
74
107
76
97
Interval after? (min)
69
62
82
91
71
84
68
75
What is the regression? equation?
? (Round to two decimal places as? needed.)
What is the best predicted time for the interval after an eruption that is 127 feet? high?
The best predicted interval time for an eruption that is 127 feet high is ____?(Round to one decimal place as? needed.)
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