Does Hypnotism Relieve Pain?The table shows the pain levels of patients before and after hypnotism. Pain level is measured on a cm scale. Assume that the two samples are randomly selected. At the 0.05 significance level, test the claim that the mean difference has increased after hypnotism.(Be sure to subtract in the same direction). Based on the hypotheses, find the following:- Test Statistic = 5.000 (Round to three decimal places.)- Critical value(s) = 1.895 (Round to three decimal places.)- p-value = __________ (Round to four decimal places.)Instructions:Shade the sampling distribution curve with the correct critical value(s) and shade the critical regions. The arrows can only be dragged to t-scores that are accurate to 1 place after the decimal point (these values correspond to the tick marks on the horizontal axis). Select from the dropdown menu to shade to the left, to the right, between, or left and right of the t-score(s).- **Shade:** Left of a value ☐. Click and drag the arrows to adjust the values.Graph Description:The graph displays a normal distribution curve centered at zero, representing a t-distribution. The horizontal axis is marked with tick marks ranging from -4 to 4. A critical region is shaded in blue on the left side of the curve starting around -1.5.- **Decision:** Select an answer ☐.- **Conclusion:** Select an answer ☐ the claim that the mean difference is less after hypnotism. The image contains a table and a section for hypothesis testing related to measurements (in centimeters) before and after a certain event or treatment. Here is the transcription:**Table: Measurement Differences**| Before (cm) | After (cm) | Difference (cm) ||-------------|------------|-----------------|| 9 | 9 | 0 || 10.7 | 6.7 | 4 || 10.9 | 9.9 | 1 || 9.9 | 5.9 | 4 || 6.6 | 3.6 | 3 || 7.5 | 4.5 | 3 || 6.8 | 3.8 | 3 || 10.2 | 8.2 | 2 |**Hypothesis Testing Section**- **What are the correct hypotheses? (Select the correct symbols and values.):** - $ H_0: \mu(d) \geq 0 $ - $ H_1: \mu(d) < 0 $ - **Original Claim = $ H_1 $.****Degrees of Freedom**- **$ df = 7 $**The table lists paired data for measurements taken before and after an event for eight subjects. The third column depicts the differences calculated by subtracting the "After" measurement from the "Before" measurement. The hypothesis testing section involves setting a null hypothesis ($ H_0 $) and an alternative hypothesis ($ H_1 $) for the differences in these measurements. The original claim is associated with the alternative hypothesis. The degrees of freedom for the test is 7.

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Description: Does Hypnotism Relieve Pain?The table shows the pain levels of patients before and after hypnotism. Pain level is measured on a cm scale. Assume that the two samples are randomly selected. At the 0.05 significance level, test the claim that the mean

Let μd is defined as the population mean difference between the pain levels of patients before and…

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Does Hypnotism Relieve Pain?

The table shows the pain levels of patients before and after hypnotism. Pain level is measured on a cm scale. Assume that the two samples are randomly selected. At the 0.05 significance level, test the claim that the mean difference has increased after hypnotism.
(Be sure to subtract in the same direction).

Based on the hypotheses, find the following:

- Test Statistic = 5.000 (Round to three decimal places.)
- Critical value(s) = 1.895 (Round to three decimal places.)
- p-value = __________ (Round to four decimal places.)

Instructions:
Shade the sampling distribution curve with the correct critical value(s) and shade the critical regions. The arrows can only be dragged to t-scores that are accurate to 1 place after the decimal point (these values correspond to the tick marks on the horizontal axis). Select from the dropdown menu to shade to the left, to the right, between, or left and right of the t-score(s).

- **Shade:** Left of a value ☐. Click and drag the arrows to adjust the values.

Graph Description:
The graph displays a normal distribution curve centered at zero, representing a t-distribution. The horizontal axis is marked with tick marks ranging from -4 to 4. A critical region is shaded in blue on the left side of the curve starting around -1.5.

- **Decision:** Select an answer ☐.

- **Conclusion:** Select an answer ☐ the claim that the mean difference is less after hypnotism.

The image contains a table and a section for hypothesis testing related to measurements (in centimeters) before and after a certain event or treatment. Here is the transcription:

**Table: Measurement Differences**

| Before (cm) | After (cm) | Difference (cm) |
|-------------|------------|-----------------|
| 9 | 9 | 0 |
| 10.7 | 6.7 | 4 |
| 10.9 | 9.9 | 1 |
| 9.9 | 5.9 | 4 |
| 6.6 | 3.6 | 3 |
| 7.5 | 4.5 | 3 |
| 6.8 | 3.8 | 3 |
| 10.2 | 8.2 | 2 |

**Hypothesis Testing Section**

- **What are the correct hypotheses? (Select the correct symbols and values.):**
- $ H_0: \mu(d) \geq 0 $
- $ H_1: \mu(d) < 0 $
- **Original Claim = $ H_1 $.**

**Degrees of Freedom**

- **$ df = 7 $**

The table lists paired data for measurements taken before and after an event for eight subjects. The third column depicts the differences calculated by subtracting the "After" measurement from the "Before" measurement. The hypothesis testing section involves setting a null hypothesis ($ H_0 $) and an alternative hypothesis ($ H_1 $) for the differences in these measurements. The original claim is associated with the alternative hypothesis. The degrees of freedom for the test is 7.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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Does Hypnotism Relieve Pain? The table shows the pain levels of patients before and after hypnotism. Pain level is measured on a cm scale. Assume that the two samples are randomly selected. At the 0.05 significance level, test the claim that the mean difference has increased after hypnotism.