he 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 0.01 significance level, test the claim that the mean difference has increased after hypnotism. (Be sure to subtract in the same direction). Before (cm) After (cm) Difference (cm) 7 3 6.2 4.2 11 6 7.3 6.3 10.1 10.1 7.5 6.5 10.9 6.9 8.6 3.6
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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 0.01 significance level, test the claim that the mean difference has increased after hypnotism.
(Be sure to subtract in the same direction).
| Before (cm) | After (cm) | Difference (cm) |
| 7 | 3 | |
| 6.2 | 4.2 | |
| 11 | 6 | |
| 7.3 | 6.3 | |
| 10.1 | 10.1 | |
| 7.5 | 6.5 | |
| 10.9 | 6.9 | |
| 8.6 | 3.6 |
What are the correct hypotheses? (Select the correct symbols and values.)
H0: Select an answer s₁² x̄₂ μ₁ μ p x̄₁ μ(d) σ₁² ? = ≠ ≥ > < ≤ Select an answer μ₁ σ₁² μ₂ μ 0 s₁² x̄₁ p x̄₂
H1: Select an answer s₂² μ μ(d) x̄₂ σ₂² x̄₁ μ₁ μ₂ p ? ≠ = < ≥ > ≤ Select an answer s₁² p 0 μ₂ x̄₂ x̄₁ σ₁² μ₁ μ
Original Claim = Select an answer H₀ H₁
df =
Based on the hypotheses, find the following:
Test Statistic = (Round to three decimal places.)
Critical value(s) = (Round to three decimal places.)
p-value = (Round to four decimal places.)
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 drop down menu to shade to the left, to the right, between or left and right of the t-score(s).
Shade: Left of a valueRight of a valueBetween two values2 regions. Click and drag the arrows to adjust the values.
Decision: Select an answer Fail to reject the null hypothesis Accept the null hypothesis Accept the alternative hypothesis Reject the null hypothesis .
Conclusion: Select an answer The sample data supports There is not sufficient evidence to warrant rejection of There is not enough evidence to support There is sufficient evidence to warrant rejection of the claim that the mean difference is less after hypnotism.
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