Question

The data in the accompanying table represent the compressive​ strength, in thousands of pounds per square inch​ (psi), of 20 samples of concrete taken two and seven days after pouring.

Sample	Two days	Seven days
1	3.205	3.54
2	2.855	3.355
3	3.135	3.605
4	3.425	4.03
5	3.16	3.43
6	3.765	4.57
7	2.68	3.805
8	3.315	3.685
9	3.205	3.59
10	3.605	3.72
11	2.895	3.25
12	3.08	3.14
13	3	4.005
14	3.035	3.595
15	2.27	3.91
16	2.205	2.28
17	2.005	2.69
18	2.985	3.475
19	2.75	3.25
20	3.065	3.63

a. At the 0.01 level of​ significance, is there evidence that the mean strength is lower at two days than at seven​ days?

Let μ1 be the mean strength at two days and let μ2 be the mean strength at seven days. State the null and alternative hypotheses.

b.The test statistic is:

c.The critical​ value(s) is(are):

d.Since the test statistic ______ (falls btwn, is >, is <, is =)the critical​ value(s), ______ (reject, do not reject) the null hypothesis H0. There is ______ evidence that the mean strength is lower at two days than at seven days.

e. What assumption is necessary about the population distribution in order to perform this​ test?

option A. It must be assumed that the distribution of the differences between the measurements is skewed.

option B. It must be assumed that the distribution of the differences between the measurements is approximately normal.

option C. It must be assumed that the distribution of the differences between the measurements is approximately uniform.

f. Find the​ p-value in​ (a) and interpret its meaning.

p value is:

Interpret the meaning of the​ p-value. Choose the correct answer below.

Option A. The probability of obtaining a sample mean difference greater than or equal to the sample mean difference of the data if the population mean strength at two days and seven days are the same

Option B. The probability of obtaining a sample mean of equal to the sample mean difference of the data for the strength for both two days and seven days

Option C. The probability of obtaining a sample mean difference less than or equal to the sample mean difference of the data if the population mean strength at two days and seven days are the same

Option D. The probability of not rejecting the null hypothesis when it is false

Answer 1