I cannot find the test statistic for the image of the problem A candy company taste-tested two chocolate bars, one with almonds and one without almonds. A panel of testers rated the bars on a scale of 0 to 5, with 5 indicating the highest taste rating. Assume the population standard deviations are equal. At the 0.05 significance level, do the ratings show a difference between chocolate bars with or without almonds?| With Almonds | Without Almonds ||--------------|------------------|| 3 | 0 || 1 | 4 || 2 | 3 || 3 | 4 || 4 | 3 || 1 | 4 || 2 | 2 |**a. State the decision rule for 0.05 significance level:** $ H_0: \mu_{With} = \mu_{Without} \quad H_1: \mu_{With} \neq \mu_{Without} $.Reject $ H_0 $ if $ t < -2.228 $ or $ t > 2.228 $.**b. Compute the test statistic.**Test statistic: \_\_\_\_**c. State your decision about the null hypothesis.**- $ \circ $ Reject $ H_0 $- $ \circ $ Do not reject $ H_0 $

For sample 1 (With almonds): xi xi-x (xi-x)2 3 1.142857 1.306122122 1 -0.85714 0.734694122…

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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I cannot find the test statistic for the image of the problem

A candy company taste-tested two chocolate bars, one with almonds and one without almonds. A panel of testers rated the bars on a scale of 0 to 5, with 5 indicating the highest taste rating. Assume the population standard deviations are equal. At the 0.05 significance level, do the ratings show a difference between chocolate bars with or without almonds?

| With Almonds | Without Almonds |
|--------------|------------------|
| 3 | 0 |
| 1 | 4 |
| 2 | 3 |
| 3 | 4 |
| 4 | 3 |
| 1 | 4 |
| 2 | 2 |

**a. State the decision rule for 0.05 significance level:** $ H_0: \mu_{With} = \mu_{Without} \quad H_1: \mu_{With} \neq \mu_{Without} $.

Reject $ H_0 $ if $ t < -2.228 $ or $ t > 2.228 $.

**b. Compute the test statistic.**

Test statistic: \_\_\_\_

**c. State your decision about the null hypothesis.**

- $ \circ $ Reject $ H_0 $
- $ \circ $ Do not reject $ H_0 $

Expert Solution

Step 1

For sample 1 (With almonds):

$x_{i}$	$x_{i} - x$	${(x_{i} - x)}^{2}$
3	1.142857	1.306122122
1	-0.85714	0.734694122
2	0.142857	0.020408122
3	1.142857	1.306122122
1	-0.85714	0.734694122
1	-0.85714	0.734694122
2	0.142857	0.020408122
Total 13		4.857142857

Then,
$\begin{array}{rcl} x_{1} & = & \frac{\sum_{i = 1}^{7} x_{i}}{7} \\ = & \frac{13}{7} \\ = & 1.857143 \end{array}$

And
$\begin{array}{rcl} s_{1} & = & \sqrt{\frac{\sum_{i = 1}^{7} {(x_{i} - x)}^{2}}{7 - 1}} \\ = & \sqrt{\frac{4.857142857}{6}} \\ = & \sqrt{0.8095238095} \\ ≃ & 0.8997 \end{array}$

Step 2

For sample 2 (Without almonds):

$x_{i}$	$x_{i} - x$	${(x_{i} - x)}^{2}$
0	-3	9
4	1	1
4	1	1
3	0	0
4	1	1
Total 15		12

Then,
$\begin{array}{rcl} x_{2} & = & \frac{\sum_{i = 1}^{5} x_{i}}{5} \\ = & \frac{15}{5} \\ = & 3 \end{array}$

And
$\begin{array}{rcl} s_{2} & = & \sqrt{\frac{\sum_{i = 1}^{5} {(x_{i} - x)}^{2}}{5 - 1}} \\ = & \sqrt{\frac{12}{4}} \\ = & \sqrt{3} \\ ≃ & 1.732 \end{array}$

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