Question

A company claims that the mean monthly residential electricity consumption in a certain region is more than 890 ​kiloWatt-hours (kWh). You want to test this claim. You find that a random sample of 69 residential customers has a mean monthly consumption of 930 kWh. Assume the population standard deviation is 125 kWh. At alphaequals0.10​, can you support the​ claim? Complete parts​ (a) through​ (e). ​(a) Identify Upper H 0 and Upper H Subscript a. Choose the correct answer below. A. Upper H 0​: muless than or equals890 Upper H Subscript a​: mugreater than890 ​(claim) B. Upper H 0​: muequals930 Upper H Subscript a​: munot equals930 ​(claim) C. Upper H 0​: muequals890 ​(claim) Upper H Subscript a​: munot equals890 D. Upper H 0​: mugreater than930 ​(claim) Upper H Subscript a​: muless than or equals930 E. Upper H 0​: mugreater than890 ​(claim) Upper H Subscript a​: muless than or equals890 F. Upper H 0​: muless than or equals930 Upper H Subscript a​: mugreater than930 ​(claim) ​(b) Find the critical​ value(s) and identify the rejection​ region(s). Select the correct choice below and fill in the answer box within your choice. Use technology. ​(Round to two decimal places as​ needed.) A. The critical values are plus or minus nothing. B. The critical value is nothing. Identify the rejection​ region(s). Select the correct choice below. A. The rejection region is zless than1.28. B. The rejection regions are zless thanminus1.28 and zgreater than1.28. C. The rejection region is zgreater than1.28. ​(c) Find the standardized test statistic. Use technology. The standardized test statistic is zequals nothing. ​(Round to two decimal places as​ needed.) ​(d) Decide whether to reject or fail to reject the null hypothesis. A. Reject Upper H 0 because the standardized test statistic is not in the rejection region. B. Fail to reject Upper H 0 because the standardized test statistic is not in the rejection region. C. Fail to reject Upper H 0 because the standardized test statistic is in the rejection region. D. Reject Upper H 0 because the standardized test statistic is in the rejection region. ​(e) Interpret the decision in the context of the original claim. At the 10​% significance​ level, there ▼ is is not enough evidence to ▼ reject support the claim that the mean monthly residential electricity consumption in a certain region ▼ is less than is different from is greater than nothing kWh. Click to select your answer(s).

Answer 1

Solution:

Given:

Claim:  the mean monthly residential electricity consumption in a certain region is more than 890 ​kiloWatt-hours (kWh)

Sample size = n = 69

Sample mean=

The population standard deviation = 125 kWh.

Level of significance = 0.10

Part a) Identify Upper H0 and Ha:

. A.    Vs (claim)

Part b) Find the critical​ value(s) and identify the rejection​ region(s).

Level of significance = 0.10

For right tailed test , find area = 1 - 0.10 = 0.90

Look in z table for area = 0.9000 or its closest area and find z value:

Area 0.8997 is closest to 0.9000 and it corresponds to 1.2 and 0.08

thus z = 1.28

B. The critical value is 1.28

Identify the rejection​ region(s).

. C. The rejection region is z greater than 1.28.

Using TI 84:

Press 2ND and VARS , select invNorm(

Enter numbers:

thus z critical value = 1.28

Part c) Find the standardized test statistic.

Use TI 84 plus calculator:

Press STAT and select TESTS

Under TESTS, select ZTest

Under ZTest select Stats

Under Stats enter numbers:

Click on Calculate and press Enter

z = 2.6581

z = 2.66

Part d) Decide whether to reject or fail to reject the null hypothesis.

Since z = 2.66 > 1.28, z test statistic value is in the rejection region thus:

D. Reject Upper H0 because the standardized test statistic is in the rejection region.

Part e) Interpret the decision in the context of the original claim.

At the 10​% significance​ level, there is enough evidence to support the claim that the mean monthly residential electricity consumption in a certain region is greater than 890 kWh.