Question

The following Excel output presents the results of a hypothesis t-test for the difference between two population means: t-Test: Two-Sample Assuming Equal Variances Sample 1 Sample 2 Mean 15.1 11.1 Variance 17.5556 24.9888 Observations 10 10 Pooled Variance ?? 0 Hypothesized Mean Difference 18 df ?? t Stat 0.0374 P(T<=t) one-tail 1.7341 t Critical one-tail 0.0748 P(T<=t) two-tail 2.1001 t Critical two-tail Notice that some values on the table are missing. (1) Calculate the pooled variance $s_p^2 = \frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{n_1 + n_2 - 2} = $ [Select] (2) Calculate the value of test statistic $t_{stat} = \frac{\bar{x}_1 - \bar{x}_2 - \Delta_0}{\sqrt{s_p^2 \left(\frac{1}{n_1} + \frac{1}{n_2}\right)}} = $[Select] (3) If the above test is with 8% level of significance, is there evidence of a difference between the two population means? [Select] (4) If the above test is with 2% level of significance, is there evidence that the first population mean is greater than the second population mean? [Select]

          The following Excel output presents the results of a hypothesis t-test for the difference between two population means:
t-Test: Two-Sample Assuming Equal Variances
Sample 1 Sample 2
Mean
15.1
11.1
Variance
17.5556
24.9888
Observations
10
10
Pooled Variance
??
0
Hypothesized Mean Difference
18
df
??
t Stat
0.0374
P(T<=t) one-tail
1.7341
t Critical one-tail
0.0748
P(T<=t) two-tail
2.1001
t Critical two-tail
Notice that some values on the table are missing.
(1) Calculate the pooled variance $s_p^2 = \frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{n_1 + n_2 - 2} = $ [Select]
(2) Calculate the value of test statistic $t_{stat} = \frac{\bar{x}_1 - \bar{x}_2 - \Delta_0}{\sqrt{s_p^2 \left(\frac{1}{n_1} + \frac{1}{n_2}\right)}} = $[Select]
(3) If the above test is with 8% level of significance, is there evidence of a difference between the two population means? [Select]
(4) If the above test is with 2% level of significance, is there evidence that the first population mean is greater than the second population mean?
[Select]

Show more…

The following Excel output presents the results of a hypothesis t-test for the difference between two population means:
t-Test: Two-Sample Assuming Equal Variances
Sample 1 Sample 2
Mean
15.1
11.1
Variance
17.5556
24.9888
Observations
10
10
Pooled Variance
??
0
Hypothesized Mean Difference
18
df
??
t Stat
0.0374
P(T<=t) one-tail
1.7341
t Critical one-tail
0.0748
P(T<=t) two-tail
2.1001
t Critical two-tail
Notice that some values on the table are missing.
(1) Calculate the pooled variance sp^2 = ((n1 - 1)s1^2 + (n2 - 1)s2^2)/(n1 + n2 - 2) = [Select]
(2) Calculate the value of test statistic tstat = (x̅1 - x̅2 - Δ0)/(√(sp^2 ((1)/(n1) + (1)/(n2)))) =[Select]
(3) If the above test is with 8% level of significance, is there evidence of a difference between the two population means? [Select]
(4) If the above test is with 2% level of significance, is there evidence that the first population mean is greater than the second population mean?
[Select]

Added by Roberto F.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert T. L.

11/02/2022

Step 1

5556 + (10 - 1)24.9888}{10 + 10 - 2} = 21.2722$ Show more…

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The following Excel output presents the results of a hypothesis t-test for the difference between two population means: t-Test: Two-Sample Assuming Equal Variances Sample 1 Sample 2 Mean 15.1 11.1 Variance 17.5556 24.9888 Observations 10 10 Pooled Variance ??? Hypothesized Mean Difference 0 df 18 t Stat ??? P(T<=t) one-tail 0.0374 t Critical one-tail 1.7341 P(T<=t) two-tail 0.0748 t Critical two-tail 2.1001 Notice that some values on the table are missing. (1) Calculate the pooled variance $s_p^2 = \frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{n_1 + n_2 - 2}$ = [Select] (2) Calculate the value of test statistic $t_{stat} = \frac{\bar{x}_1 - \bar{x}_2 - \Delta_0}{s_p \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}$ = [Select] (3) If the above test is with 8% level of significance, is there evidence of a difference between the two population means? [Select] (4) If the above test is with 2% level of significance, is there evidence that the first population mean is greater than the second population mean? [Select]

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Transcript

00:01 Hey there, welcome to numerade.

00:03 So we are giving three separate questions here, and we're asked to find the following answers using the anova summary table.

00:13 So let us do the first one here, question one.

00:17 We're asked, what can you conclude about the equality of the population means? so we first have to pay attention to the significance level, which is given to us as 0 .05.

00:32 To conclude, we will need to accept or reject the null hypothesis based on our p value.

00:39 So the p value that is given to us here on a table in the upper right is 0 .264.

00:48 So therefore, a conclusion here would be since our p value is greater than our significance level, we accept the null hypothesis.

01:06 Except the null hypothesis.

01:10 So therefore, this will correlate to a value of, to a choice of choice a, okay, since the p value is greater than the significance level.

01:26 So choice a is our answer.

01:35 Okay, let's move on to question two here.

01:38 Question two, this is a partially completed one -way annova table.

01:43 So the total number of observations for this anova procedure is.

01:48 So the total number of observations, we're going to be looking at the degrees of freedom formula.

02:15 So for the between, the degrees of freedom formula will take the number of observations here.

02:28 It's going to be basically k minus 1, right? so we have k minus 1 and for the within, we have our sample size minus k.

02:52 And for our total, we can just know the total sample size here, where the degrees of freedom equals n minus 1.

03:07 So you can see our degrees of freedom here is 21.

03:11 So we have 21 equals n minus 1, making n equals 22.

03:20 Okay, so our answer here is 22, making our answer choice as d.

03:32 All right...

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