Question

A manufacturer wants to increase the shelf life of a line of cake mixes. Past records indicate that the average shelf life of the mix is 216 days. After a revised mix has been developed, a sample of nine boxes of cake mix gave these shelf lives (in days): 215, 217, 218, 219, 216, 217, 217, 218, and 218. Using α = 0.025, has the shelf life of the cake mix increased?

Select one:

a.

Yes, because computed p is greater than the level of significance.

b.

Yes, because computed p is less than the level of significance.

c.

No, because computed p lies in the region of acceptance.

d.

No, because 217.24 is quite close to 216.

Answer 1

Given Data

Sample mean X = 217.22(calculated from given sample)

Sample standard deviation s = 1.20 (calculated)

Sample size n = 9 ,

Degree of freedom = 9-1 = 8

Level of significance = α = 0.025

(1) Null and Alternative hypothesis

The following Null and Alternative hypothesis need to be tested:

Ho: µ = 216

Ha: µ > 216

This corresponds to a right-tailed test, for which a t-test will be done for unknown population standard deviation.

(2) Rejection Region.

Based on the information provided, the significance level is α=0.05, and the critical value for a right-tailed test is tc​=2.306 using Excel Formula =T.INV(0.975,8)

The rejection region for this right-tailed test is R =t>2.306

(3) Test statistics

The t-statistic is computed as follows

(4) Decision about the null hypothesis

Since it is observed that t = 3.05 which is greater than critical value tc= 2.306, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p = 0.0079,using Excel formula

=1-T.DIST(3.05,8,TRUE) and since p value is less than α= 0.025, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to support the claim that the population mean µ is greater than 216, at the 0.025 significance level.

So answer will be "b" i.e, Yes ,because computed p is less than level of significance.