I need help with the following MCQs. Please provide explanation(s) for your answers:

1) In a test of statistical significance, thep-value tells us:

a) if the null hypothesis is true.

b) if the alternate hypothesis is true.

c) the largest level of significance at which the null hypothesis can be rejected.

d) the smallest level of significance at which the null hypothesis can be rejected.

2) All else being equal, which of the following is true?

a) As you increase the sample size, you will decrease thep-value.

b) As you increase the standard deviation, thelevel will increase.

c) As you increase thelevel, thep-value decreases.

d) As the sample mean gets further from the mean, thep-value will increase.

3) A shipment of 1000 cartons of fruit arrives at a distribution center with a nominal weight of 10 lbs per carton. A sample of cartons is selected and weighed. The average weight of the sample is 9.7 lbs. From past shipments, it is known that the standard deviation of weight among cartons is 2 lbs. The auditor wishes to test the hypothesis that the average weight of the cartons matches the nominal value vs. that the cartons are underweight at= 0.05. Thep-value for the test was 0.047. Which of the following is correct?

a) There is a 4.7% chance that the cartons are underweight.

b) 4.7% of cartons are underweight.

c) There is 4.7% chance that the sample weight would be 9.7 lbs (or less) if the nominal weight were correct.

d) There is 4.7% change that the nominal weight of 10 lbs is more than the sample mean of 9.7 lbs.

4) A shipment of 1000 cartons of fruit arrives at a distribution center with a nominal weight of 10 lbs per carton. A sample of 20 cartons is selected and weighed. The average weight of the sample is 9.8 lbs. From past shipments, it is known that the standard deviation of weight among cartons is 2 lbs. The auditor wishes to test the hypothesis that the average weight of the cartons matches the nominal value vs. that the cartons are underweight at= 0.05. The test statistic (z-score) is:

a) -0.10

b) -0.45

c) -1.0

d) -1.65