A researcher randomly selects 6 fathers who have adult sons and records the fathers' and sons'...
A researcher randomly selects 6 fathers who have adult sons and records the fathers' and sons' heights to obtain the data shown in the table below. Test the claim that sons are taller than their fathers at the a= 0.10 level of significance. The normal probability plot and boxplot indicate that the differences are approximately normally distributed with no outliers so the use of a paired t-test is reasonable.
|
Observation |
1 |
2 |
3 |
4 |
5 |
6 |
|
|---|---|---|---|---|---|---|---|
|
Height of father (in inches) |
72.272.2 |
68.368.3 |
67.467.4 |
68.468.4 |
66.466.4 |
73.973.9 |
|
|
Height of son (in inches) |
76.076.0 |
71.971.9 |
71.771.7 |
70.870.8 |
67.167.1 |
77.1 |
what is the test statistic?
t=?
what are the critical values?
Homework Answers
![(a) The computation table 72.276 68.3 71.9 67.4 71.74.3 68.470.8 66.4 67.1 73.9 77.1 14.44 12.96 18.49 5.76 0.49 10.24 3.6 2.4 0.7 3.2 d18 62.38 The formula for calculating the popul ati on mean difference is -18) Therefore, the popul ati on mean of the differences is (b) The stan dard deviati on of the difference is 2 (-18) 62.38- 324 62.38 62.38-54] 1(8.38) V1.676 1.294604 sa 1.294604 Therefore, the stan dard deviation of the differences is s, 1.294604](http://img.homeworklib.com/questions/8b055830-6f67-11ea-be3a-330e981fa99e.png?x-oss-process=image/resize,w_560)
![(c) Step1: The null and alternative hypotheses are as follows vefsus Step2: Decide the test stati stic and the level of significance The level of significance is α-010 The critical value of t is to n5 -1.476 Step3: State the decision Rule Reject Ho if t>1.476 otherwise do not reject Ho Step4: Calculate the value of test statistic The paired difference experiment produced the following results nn -6, 7, 69.43333, 7,-72.43333, n3 Sn 1.294604 0.10,5 1.294604 1.294604 2.44949 0.52852 SEp 0.52852 The formula for calculating the test stati stic is SE 0.52852 -5.67623 PI=56762] Step5: The P- value Approach P-value - P(>5.6762) (1-P(t < 5.6762)) 10.998819) 0.001181 P-value 10.00 1 1 81| < α-0. 10. We reject the null hypothesis Ho Conclusion Step6: Compare with the critical value and make a decision Since, the P-value-0.001 181 < α-0.10. We reject the null hypothesis Ho Since, the t-test statistic ist 5.6762 > o,s1.476. We reject the null hypothesis Ho Hence, we conclude that there is sufficient evi dence to reject the null hypothesis that μ,-0 There is sufficient evi dence to support the claim that the mean difference between the heights of sons are taller than their fathers at the 10% level of significance](http://img.homeworklib.com/questions/8b596500-6f67-11ea-821a-71a6d02c94e1.png?x-oss-process=image/resize,w_560)
Add Answer to:
A researcher randomly selects 6 fathers who have adult sons and
records the fathers' and sons'...
A researcher randomly selects 6 fathers who have adult sons and records the fathers' and sons'...
A researcher randomly selects 6 fathers who have adult sons and records the fathers' and sons' heights to obtain the data shown in the table below. Test the claim that sons are taller than their fathers at the alpha equals 0.10α=0.10 level of significance. The normal probability plot and boxplot indicate that the differences are approximately normally distributed with no outliers so the use of a paired t-test is reasonable. Observation 1 2 3 4 5 6 Height of father...
A researcher randomly selects 6 fathers who have adult sons and records the fathers' and sons'...
A researcher randomly selects 6 fathers who have adult sons and records the fathers' and sons' heights to obtain the data shown in the table below. Test the claim that sons are taller than their fathers at the alpha α=0.10level of significance. The normal probability plot and boxplot indicate that the differences are approximately normally distributed with no outliers so the use of a paired t-test is reasonable. Observation 1 2 3 4 5 6 Height of father (in inches)...
A researcher randomly selects 6 fathers who have adult sons and records the fathers' and sons'...
A researcher randomly selects 6 fathers who have adult sons and records the fathers' and sons' heights to obtain the data shown in the table below. Test the claim that sons are taller than their fathers at the alpha equals 0.10α=0.10 level of significance. The normal probability plot and boxplot indicate that the differences are approximately normally distributed with no outliers so the use of a paired t-test is reasonable. Observation 1 2 3 4 5 6 Height of father...
What are the hypotheses for the t test? Find the test statistic. Find the critical value(s)...
What are the hypotheses for the t test?
Find the test statistic.
Find the critical value(s)
What is the correct conclusion of the hypothesis?
A researcher randomly selects 6 fathers who have adult sons and records the fathers' and sons' heights to obtain the data shown in the table below. Test the claim that sons are taller than their fathers at the o-0.10 level of significance. The normal probability plot and boxplot indicate that the differences are approximately normally distributed...
9. To test the belief that sons are taller than their fathers, a student randomly selects I3 fathers who have adult male children. She records the height of both the father and son in inches and...
9. To test the belief that sons are taller than their fathers, a student randomly selects I3 fathers who have adult male children. She records the height of both the father and son in inches and obtains the following data: Height of father, X 70.3 67.1 709 66.8 Height of son, Y 74.1 69.2 669 692 689 70.2 70.4 728 70.4 71.8 一81-9 | 10 | 11 | 12 | 13 Height of father, 70.1 69.9 70.8 70.2 704 724...
To test the belief that sons are taller than their fathers, a student randomly selects 13...
To test the belief that sons are taller than their fathers, a student randomly selects 13 fathers who have adult male children. She records the height of both the father and son in inches and obtains the following data. Are sons taller than their fathers? Use the α=0.10 level of significance. Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers. Height of Father Height of Son 71.5 ...
To test the belief that sons are taller than their fathers, a student randomly selects 13...
To test the belief that sons are taller than their fathers, a student randomly selects 13 fathers who have adult male children. She records the height of both the father and son in inches and obtains the following data. Are sons taller than their fathers? Use the alphaαequals=0.050.05 level of significance. Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers. LOADING... Click the icon to view the table...
To test the belief that sons are taller than their fathers, a student ran- domly selects 13 fathe...
To test the belief that sons are taller than their fathers, a student ran- domly selects 13 fathers who have adult male children. She records the height (in inches) of both the father and the son in the following table. Are sons taller than their fathers? NOTE: A normal probability plot indicated that the differences (X -Y) are approximately normally distributed with no outliers. 70.4 71.8 70.1 70.2 70.4 69.3 eight of Father, Y eight of Son, X eight of...
To test the belief that sons are taller than their fathers, a student randomly selects 13...
To test the belief that sons are taller than their fathers, a student randomly selects 13 fathers who have adult male children. She records the height of both the father and son in inches and obtains the following data. Are sons taller than their fathers? Use the a= 0.01 level of significance. Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers. Click here to view the table of...
To test the belief that sons are taller than their fathers, a student randomly selects 13...
To test the belief that sons are taller than their fathers, a student randomly selects 13 fathers who have adult male children. She records the height of both the father and son in inches and obtains the following data. Are sons taller than their fathers? Use the a = 0.05 level of significance. Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers. Click the icon to view the...
What are the hypotheses for the t test?
Find the test statistic.
Find the critical value(s)
What is the correct conclusion of the hypothesis?
A researcher randomly selects 6 fathers who have adult sons and records the fathers' and sons' heights to obtain the data shown in the table below. Test the claim that sons are taller than their fathers at the o-0.10 level of significance. The normal probability plot and boxplot indicate that the differences are approximately normally distributed...
9. To test the belief that sons are taller than their fathers, a student randomly selects I3 fathers who have adult male children. She records the height of both the father and son in inches and obtains the following data: Height of father, X 70.3 67.1 709 66.8 Height of son, Y 74.1 69.2 669 692 689 70.2 70.4 728 70.4 71.8 一81-9 | 10 | 11 | 12 | 13 Height of father, 70.1 69.9 70.8 70.2 704 724...
To test the belief that sons are taller than their fathers, a student ran- domly selects 13 fathers who have adult male children. She records the height (in inches) of both the father and the son in the following table. Are sons taller than their fathers? NOTE: A normal probability plot indicated that the differences (X -Y) are approximately normally distributed with no outliers. 70.4 71.8 70.1 70.2 70.4 69.3 eight of Father, Y eight of Son, X eight of...
To test the belief that sons are taller than their fathers, a student randomly selects 13 fathers who have adult male children. She records the height of both the father and son in inches and obtains the following data. Are sons taller than their fathers? Use the a= 0.01 level of significance. Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers. Click here to view the table of...
To test the belief that sons are taller than their fathers, a student randomly selects 13 fathers who have adult male children. She records the height of both the father and son in inches and obtains the following data. Are sons taller than their fathers? Use the a = 0.05 level of significance. Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers. Click the icon to view the...
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