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In: Statistics and Probability

The manufacturer of an over-the-counter pain reliever claims that its product brings pain relief to headache...

The manufacturer of an over-the-counter pain reliever claims that its product brings pain relief to headache suffers in less than 3.5 minutes, on average. In order to be able to make this claim in its television advertisements, the manufacturer was required by a particular television network to present statistical evidence in support of the claim. The manufacturer reported that for a sample of 50 headache sufferers, the mean time to relief was 3.3 minutes and the standard deviation was 66 seconds. Use ?=0.05α=0.05.

(a) State null and alternative hypothesis.

(b) Calculate the value of test-statistic.

(c) Obtain the p-value for the test.

(d) Write your conclusion based on the data.

(e) Construct 95% confidence interval for the mean time of pain relief.

PLEASE SHOW DETAILED WORK, thank you :)

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