Question

Consider the following competing hypotheses and accompanying sample data. (You may find it useful to reference the appropriate table: z table or t table) H0: ?1 - ?2 = 6 HA: ?1 - ?2 ? 6 x?1 = 59, x?2 = 45 s1 = 23.6, s2 = 17.3 n1 = 20, n2 = 15 Assume that the populations are normally distributed with equal variances. a-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) Test statistic a-2. Find the p-value. p-value < 0.01 0.01 ? p-value < 0.02 0.02 ? p-value < 0.05 0.05 ? p-value < 0.10 p-value ? 0.10 b. At the 10% significance level, can you conclude that the difference between the two means differs from 6? H0. At the 10% significance level, we conclude that the difference between the means differs from 6.

          Consider the following competing hypotheses and accompanying sample data. (You may find it useful to reference the appropriate table: z table or t table)

H0: ?1 - ?2 = 6
HA: ?1 - ?2 ? 6

x?1 = 59, x?2 = 45
s1 = 23.6, s2 = 17.3
n1 = 20, n2 = 15

Assume that the populations are normally distributed with equal variances.

a-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

Test statistic

a-2. Find the p-value.

p-value < 0.01
0.01 ? p-value < 0.02
0.02 ? p-value < 0.05
0.05 ? p-value < 0.10
p-value ? 0.10

b. At the 10% significance level, can you conclude that the difference between the two means differs from 6?

H0. At the 10% significance level, we conclude that the difference between the means differs from 6.

Show more…

Consider the following competing hypotheses and accompanying sample data. (You may find it useful to reference the appropriate table: z table or t table)

H0: ?1 - ?2 = 6
HA: ?1 - ?2 ? 6

x?1 = 59, x?2 = 45
s1 = 23.6, s2 = 17.3
n1 = 20, n2 = 15

Assume that the populations are normally distributed with equal variances.

a-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

Test statistic

a-2. Find the p-value.

p-value < 0.01
0.01 ? p-value < 0.02
0.02 ? p-value < 0.05
0.05 ? p-value < 0.10
p-value ? 0.10

b. At the 10% significance level, can you conclude that the difference between the two means differs from 6?

H0. At the 10% significance level, we conclude that the difference between the means differs from 6.

Added by Cindy A.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Federico Castro

05/16/2022

Step 1

6, s_2 = 17.3, n_1 = 20, n_2 = 15 \] Substitute the values into the formula: \[ t = \frac{(51 - 45) - (42 - 42)}{\sqrt{\frac{23.6^2}{20} + \frac{17.3^2}{15}}} \] \[ t = \frac{6}{\sqrt{28.09 + 20.49}} \] \[ t = \frac{6}{\sqrt{48.58}} \] \[ t = \frac{6}{6.966} Show more…

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Consider the following competing hypotheses and accompanying sample data: (You may find it useful to reference the appropriate table: z table or t table) H0: μ1 - μ2 = 6 HA: μ1 - μ2 ≠ 6 x̄1 = 59, x̄2 = 45 s1 = 23.6, s2 = 17.3 n1 = 20, n2 = 15 Assume that the populations are normally distributed with equal variances. a-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) Test statistic a-2. Find the p-value. p-value < 0.01 0.01 ≤ p-value < 0.02 0.02 ≤ p-value < 0.05 0.05 ≤ p-value < 0.10 p-value ≥ 0.10 b. At the 10% significance level, can you conclude that the difference between the two means differs from 6? H0. At the 10% significance level, we conclude that the difference between the means differs from 6.

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Transcript

00:01 In this situation they give us two samples.

00:04 Here's the data for the two samples and they have a hypothesis.

00:08 The hypothesis is the difference in the means of the two samples is six and the alternate hypothesis is that it is different from six.

00:19 So what we're going to do is we're going to do a two sample test for the difference in this situation.

00:27 So to do that we can use our calculate.

00:31 In the statistical part of it.

00:33 If you have a graphical calculator like the t -i -84, for example, which is a very popular calculator, you can do it.

00:40 In this case, so for example, in t -i -84, we can go to the statistic part of it, stat, and go to tests.

00:55 And because of the small size of the samples, which in this case is 15 and 20, you want to do a two -sample t -test.

01:09 T -test.

01:10 Now, because the calculator only does comparisons when the difference is zero, the technique that you do is you add to the smaller one, you just add, you just add six.

01:25 Because usually the calculator only compares that if the difference is zero.

01:30 So you just add six to this value when you input it in the calculator, and that's all there is to it.

01:35 So in x2 instead of inputting 45, we're going to input 45 plus 6 is 51.

01:43 And everything else is the same.

01:45 So the calculator is going to ask you to input all this data.

01:49 So we do that.

01:52 After the inputting the data, the calculator asks you what is the alternate hypothesis...

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