Imagine a researcher presented a null hypothesis that in a certain community, the average energy expenditure of residents is at least 2,100 calories per day. He randomly sampled 100 residents in that particular community. He computed a negative test statistic and the associated p-value was 0.08. Given a 90% confidence level, he should conclude:

a. The average energy expenditure is greater than 2,100 calories per day
b. The average energy expenditure is less than 2,100 calories per day
c. The average energy expenditure is not equal to 2,100 calories per day
d. Fail to reject the null hypothesis
e. None of the above

Did i word this correctly?

ANSWER IS B
The p value is less than the significance level therefore we reject the null hypothesis and conclude the alternative to be true. While the null hypothesis is the average energy expenditure of residence is at least 2,100 calories per day, the alternative is the average energy expenditure of residents is less than 2,100 calories per day which is supported.

Yes, you have worded it correctly. The correct answer is b. The researcher should conclude that the average energy expenditure is less than 2,100 calories per day. Since the p-value of 0.08 is greater than the significance level of 0.10 (1 - confidence level of 0.90), the null hypothesis cannot be rejected. Therefore, the alternative hypothesis, which states that the average energy expenditure is less than 2,100 calories per day, is not supported.

Yes, you have worded the question correctly. However, the answer you provided is incorrect.

To determine the correct answer, we need to compare the p-value to the significance level (alpha) for the hypothesis test. In this case, the significance level is not given, so we'll assume it is the conventional value of 0.05.

Since the p-value (0.08) is greater than the significance level (0.05), we fail to reject the null hypothesis. This means that we do not have enough evidence to support the alternative hypothesis, which states that the average energy expenditure of residents is less than 2,100 calories per day.

Therefore, the correct answer is d. Fail to reject the null hypothesis.