Question

In: Statistics and Probability

For a hypothesis test, where ?0:?1=0 and ?1:?1≠0, and using ?=0.01 , give the following:

Consider the data set below.

x 22 99 88 44 99 99
y 66 44 88 55 77 11

For a hypothesis test, where ?0:?1=0 and ?1:?1≠0, and using ?=0.01 , give the following:

(a) The test statistic ?=

(b) The degree of freedom ??=

(c) The rejection region |?|>

The final conclustion is

A. There is not sufficient evidence to reject the null hypothesis that ?1=0 β 1 = 0 .

B. We can reject the null hypothesis that ?1=0 β 1 = 0 and accept that ?1≠0 β 1 ≠ 0 .

Solutions

Expert Solution

The statistical software output for this problem is:

On the basis of above output:

a) t = -0.4213

b) df = 4

c) Rejection region: |t| > 4.604

Final conclusion: There is not sufficient evidence to reject the null hypothesis that ?1=0


Related Solutions

Consider the following hypothesis test. H0: μd ≤ 0 Ha: μd > 0 (a) The following...
Consider the following hypothesis test. H0: μd ≤ 0 Ha: μd > 0 (a) The following data are from matched samples taken from two populations. Compute the difference value for each element. (Use Population 1 − Population 2.) Element Population Difference 1 2 1 21 18 2 28 25 3 18 16 4 20 19 5 26 25 (b) Compute d. (c) Compute the standard deviation sd. Conduct a hypothesis test using α = 0.05. Calculate the test statistic. (Round...
Consider the following hypothesis test. H0: μd ≤ 0 Ha: μd > 0 (a) The following...
Consider the following hypothesis test. H0: μd ≤ 0 Ha: μd > 0 (a) The following data are from matched samples taken from two populations. Compute the difference value for each element. (Use Population 1 − Population 2.) Element Population Difference 1 2 1 21 20 2 28 28 3 18 18 4 20 18 5 26 24 (b) Compute d. (c) Compute the standard deviation sd. (d) Conduct a hypothesis test using α = 0.05. Calculate the test statistic....
Consider the following hypothesis test. H0: μd ≤ 0 Ha: μd > 0 (a) The following...
Consider the following hypothesis test. H0: μd ≤ 0 Ha: μd > 0 (a) The following data are from matched samples taken from two populations. Compute the difference value for each element. (Use Population 1 − Population 2.) Element Population Difference 1 2 1 21 21 2 28 28 3 18 16 4 20 18 5 26 25 (b) Compute d. (c) Compute the standard deviation sd. (d) Conduct a hypothesis test using α = 0.05. Calculate the test statistic....
A 0.01 significance level is used for a hypothesis test of the claim that when parents...
A 0.01 significance level is used for a hypothesis test of the claim that when parents use a particular method of gender​ selection, the proportion of baby girls is different from 0.5. Assume that sample data consists of 78 girls in 169 ​births, so the sample statistic of six thirteenths results in a z score that is 1 standard deviation below 0. Complete parts​ (a) through​ (h) below. A . Identify the null hypothesis and the alternative hypothesis. Choose the...
A 0.01 significance level is used for a hypothesis test of the claim that when parents...
A 0.01 significance level is used for a hypothesis test of the claim that when parents use a particular method of gender selection, the proportion of baby girls is different from 0.5. Assume that sample data consists of 78 girls in 169 births, so the sample statistic of 6/13 results in a z score that is 1 standard deviation Complete parts (a) through (h) below a. identify the null hypothesis and alternative hypothesis. b. what is the value of a?...
A 0.01 significance level is used for a hypothesis test of the claim that when parents...
A 0.01 significance level is used for a hypothesis test of the claim that when parents use a particular method of gender? selection, the proportion of baby girls is less than 0.5. Assume that sample data consists of 66 girls in 144 ?births, so the sample statistic of StartFraction 11 Over 24 EndFraction results in a z score that is 1 standard deviation below 0. Complete parts? (a) through? (h) below. Click here to view page 1 of the Normal...
If a hypothesis test turns out to be statistically significant at the significance level of 0.01...
If a hypothesis test turns out to be statistically significant at the significance level of 0.01 (meaning reject the null hypothesis at 0.01 significance level), it will also be significant at:  Circle your answer(s)​    Significant level of 0.05   Significant level of 0.001 Significant level of 0.005 Significant level of 0.1 Which p-value would provide more evidence against the null hypothesis:             p-value of 0.02 and p-value of 0.04. Explain your answer.​    ATM machines must be stocked enough cash to satisfy customers...
We wish to test the hypothesis that μ≥0 at the 4% level using a sample of...
We wish to test the hypothesis that μ≥0 at the 4% level using a sample of 60 observations. The rejection region for this test is: Below -1.75 Above 1.75 Below -2.05 Above 2.05
Consider the following hypothesis test. H0: u 1 -u  2= 0 Ha: u1 -u  2≠ 0 The following...
Consider the following hypothesis test. H0: u 1 -u  2= 0 Ha: u1 -u  2≠ 0 The following results are from independent samples taken from two populations. Sample 1 Sample 2 n 1 = 35 n 2 = 40 x 1 = 13.6 x 2 = 10.1 s 1 = 5.8 s 2 = 8.1 a. What is the value of the test statistic (to 2 decimals)? b. What is the degrees of freedom for the t distribution? (Round down your answer...
A) In a​ one-tail hypothesis test where you reject H 0 only in the lower ​tail,...
A) In a​ one-tail hypothesis test where you reject H 0 only in the lower ​tail, what is the p value if Z STAT = -1.68? Round decimal to four places B) In a​ one-tail hypothesis test where you reject H0 only in the upper​ tail, what is the critical value of the​ t-test statistic with 48 degrees of freedom at the 0.10 level of​ significance? The critical value of the t-test statistic is____ ? Round 4 decimal places C)...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT