Question

A test was conducted for two overnight mail delivery services. Two samples of identical deliveries were set up so that both delivery services were notified of the need for a delivery at the same time. The hours required to make each delivery follow. Do the data shown suggest a difference in the delivery times for the two services? Use a .05 level of significance for the test.

Delivery	Service 1	Service 2
1	24.5	28.0
2	26.0	25.5
3	28.0	32.0
4	21.0	20.0
5	18.0	19.5
6	36.0	28.0
7	25.0	29.0
8	21.0	22.0
9	24.0	23.5
10	26.0	29.5
11	31.0	30.0

What is the z-statistic (to 2 decimals)? Enter negative values as negative number, if necessary.

What is the p-value (to 4 decimals)?

Conclude: reject the null hypothesis/ fail to reject the null hypothesis

There: is/is not a statistical difference

Answer 1

The data is :

Since the population standard deviation is unknown we would not use the z statistic but the t statistic. The t-statistic is computed as follows:

The p-value is p = 0.7680

Since it is observed that ∣t∣=0.299≤tc​=2.086, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p=0.768, and since p=0.768≥0.05, it is concluded that the null hypothesis is not rejected.

Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ1​ is different than μ2​, at the 0.05 significance level.

Not a statistical difference

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