Question

John is a physician who is interested in learning to what extent running affects heart rate in 18-25 year-olds. John believes that only a minority of 18-25 year-olds will experience a heart rate of at least 120 beats per minute (bpm) after running a mile. John gets a random sample of people aged from 18-25 to run a mile and records their heart rate. He finds that 40% have a heart rate of at least 120 bpm. He conducts a hypothesis test.

The p-value for the test is calculated to be 0.143.

Which of the statements below are correct interpretations of the p-value? You should choose all that are correct interpretations.

Question 15 options:

	The p-value is the proportion of times in repeated sampling that the alternative hypothesis is true.
	If we repeat the hypothesis test many times, the p-value is the proportion of times our test statistic will be close to the expected value of the null distribution.
	This p-value suggests that based on this sample there is strong evidence that the null model is not compatible with the data.
	The p-value is the probability that the null hypothesis is true.
	This p-value suggests that based on this sample there is little evidence that the null model is not compatible with the data.
	The p-value is the probability of obtaining a sample result at least as or more in favor of the alternative hypothesis if the null hypothesis is true.

Answer 1

Here are event is that after running a mile the heart rate is at least 120 bpm.

After sampling and experimenting it is found that 40% had a heart rate to be at least 120 bpm.

Since nothing is given we assume that having at least 120 bpm or not having is same.So our null proportion for heart rate being at least 120 bpm is 50%

Null: p = 50%

Alternative : p 50%

p-value is the probabiltiy of null hypothesis being true and if p-value <level of significance then we reject the null hypothesis or have sufficient evidence to reject it.

If here we take level of significance = 0.1 = 10%

p -value = 0.143

Since p-value > 10% , we do not reject the null hypothesis.

Which of the statements below are correct interpretations of the p-value? You should choose all that are correct interpretations.

Question 15 options:

	The p-value is the proportion of times in repeated sampling that the alternative hypothesis is true. Its null hypothesis probability.
	If we repeat the hypothesis test many times, the p-value is the proportion of times our test statistic will be close to the expected value of the null distribution. expected value of null hypothesis being true. = np where p = p-value and 'n' would be times of hypothesis tests.
	This p-value suggests that based on this sample there is strong evidence that the null model is not compatible with the data. we are not rejecting so there is compatibility wilh nul model
	The p-value is the probability that the null hypothesis is true.
	This p-value suggests that based on this sample there is little evidence that the null model is not compatible with the data. there is little evidence that is why we are not rejecting it.
	The p-value is the probability of obtaining a sample result at least as or more in favor of the alternative hypothesis if the null hypothesis is true. if null hypothesis is true with high probability then it will not be in favor of alternative hypothesis.