Jacqueline, a medical researcher, would like to make the claim that a newly developed prescription medication for headaches gives patients relief in 61 minutes or less, on average. Jacqueline samples 12 users of the medication and obtains a sample mean of 55 minutes. At the 1% significance level, should Jacqueline reject or fail to reject the null hypothesis given the sample data below? H0:μ=61 minutes; Ha:μ<61 minutes α=0.01 (significance level) test statistic=−1.99Answer for the above question:Do not reject the null hypothesis because the p-value 0.0233 is greater than the significance level α=0.01.Jacqueline is making the claim that the average time it takes the headache medication to work is less than 61 minutes. Therefore, this is a left-tailed test because of “less than". Since this is a left-tailed test, α and p-value will be areas on the left side of the distribution.In making the decision to reject or not reject H0, recall the criterion for comparing the p−value to α. If p≤α, reject H0. Since the p-value 0.0233 is greater than the significance level α=0.01, do not reject the null hypothesis. QUESTION:Using the information above, choose the correct conclusion for this hypothesis test. Select the correct answer below: 1) There is sufficient evidence to conclude that the headache medication gives patients relief in 61 minutes or less, on average. 2) There is NOT sufficient evidence to conclude that the headache medication gives patients relief in 61 minutes or less, on average. 3.) There is sufficient evidence to conclude that the headache medication gives patients relief in 55 minutes or less, on average. 4.) There is NOT sufficient evidence to conclude that the headache medication gives patients relief in 55 minutes or less, on average.

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Asked Oct 8, 2019
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Jacqueline, a medical researcher, would like to make the claim that a newly developed prescription medication for headaches gives patients relief in 61 minutes or less, on average. Jacqueline samples 12 users of the medication and obtains a sample mean of 55 minutes. 

At the 1% significance level, should Jacqueline reject or fail to reject the null hypothesis given the sample data below?
 

  • H0:μ=61 minutes; Ha:μ<61 minutes
     
  • α=0.01 (significance level)
     
  • test statistic=−1.99

Answer for the above question:

Do not reject the null hypothesis because the p-value 0.0233 is greater than the significance level α=0.01.

Jacqueline is making the claim that the average time it takes the headache medication to work is less than 61 minutes. Therefore, this is a left-tailed test because of “less than". Since this is a left-tailed test, α and p-value will be areas on the left side of the distribution.

In making the decision to reject or not reject H0, recall the criterion for comparing the p−value to α. If p≤α, reject H0. 

Since the p-value 0.0233 is greater than the significance level α=0.01, do not reject the null hypothesis. 

QUESTION:

Using the information above, choose the correct conclusion for this hypothesis test. 

Select the correct answer below:

 

1) There is sufficient evidence to conclude that the headache medication gives patients relief in 61 minutes or less, on average.

 

2) There is NOT sufficient evidence to conclude that the headache medication gives patients relief in 61 minutes or less, on average.

 

3.) There is sufficient evidence to conclude that the headache medication gives patients relief in 55 minutes or less, on average.

 

4.) There is NOT sufficient evidence to conclude that the headache medication gives patients relief in 55 minutes or less, on average.

 

 

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Rejection rule:...

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If p-value significance level, reject the null hypothesis If p-value significance level, do not reject the null hypothesis

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