You believe that the mean annual water usage of households in a certain region i

Question

You believe that the mean annual water usage of households in a certain region is less than 127,000 gallons. You find that a random sample of 35 households has a mean water usage of 125,070 gallons with a standard deviation of 6237 gallons. You conduct a statistical experiment where H0: 127,000 Ha:<127,000. At alpha±=0.01, z0= -2.33 and z almost =-1.83; so, you cannot reject H0. You believe that H0 is not valid. Which of the following allows you to reject H0? Explain your reasoning. (A) Use the same values, but increase alpha± from 0.01 to 0.02 (B) Use the same values, but increase alpha± from 0.01 to 0.05 (c) Use the same values, but increase n from 35to 45 (d) Use the same values, but increase n from 35 to 70 (a) Find the critical value(s). Select the correct choice below and fill in the answer box within your choice. (Round to two decimal places as needed.) A) The critical values are ±z 0z0=± B) The critical value is z 0z0= Find the standardized test statistic. The standardized test statistic is z= (Round to two decimal places as needed.) Increasing alphaα from 0.01 to 0.02 the H0 because the standardized test statistic in the rejection region. (b) Find the critical value(s). Select the correct choice below and fill in the answer box within your choice. (Round to two decimal places as needed.) A.The critical value is z0= B.The critical values are ±z 0z0=± Find the standardized test statistic. The standardized test statistic is zs= (Round to two decimal places as needed.) Increasing alphaα from 0.01 to 0.05 the H0 because the standardized test statistic in the rejection region. (C) Find the critical value(s). Select the correct choice below and fill in the answer box within your choice. (Round to two decimal places as needed.) A. The critical value is z0= B. The critical values are ±z0=± . Find the standardized test statistic. The standardized test statistic is z= (Round to two decimal places as needed.) Increasing n from 35 to 45 the H0 becausethe standardized test statistic in the rejection region. (D) Find the critical value(s). Select the correct choice below and fill in the answer box within your choice. (Round to two decimal places as needed.) A.The critical values are plus or ± z0=± . B.The critical value is z0= . Find the standardized test statistic. The standardized test statistic is z= (Round to two decimal places as needed.) Increasing n from 35 to 70 the H0 because the standardized test statistic in the rejection region.

Explanation / Answer

Which of the following allows you to reject H0? Explain your reasoning.

(A) Use the same values, but increase alpha± from 0.01 to 0.02

Find the critical value(s).

The critical value at alpha = 0.02 is -2.05

The standardized test statistic is z will be unchanged and z = -1.83

As, standardized test statistic (-1.83) > critical value (-2.05), the standardized test statistic is not in the rejection region and we cannot reject H0

(B) Use the same values, but increase alpha± from 0.01 to 0.05

Find the critical value(s).

The critical value at alpha = 0.05 is -1.64

The standardized test statistic is z will be unchanged and z = -1.83

As, standardized test statistic (-1.83) < critical value (-1.64), the standardized test statistic is in the rejection region and we reject H0.

(C) Use the same values, but increase n from 35to 45

Find the critical value(s).

The critical values will be unchanged and z0= -2.33

The standardized test statistic

Standard error of the mean = 6237/sqrt(45) = 929.76

z= (125070 - 127000)/929.76 = -2.08

As, standardized test statistic (-2.08) > critical value (-2.33), the standardized test statistic is not in the rejection region and we cannot reject H0

(D) Use the same values, but increase n from 35 to 70

Find the critical value(s).

The critical values will be unchanged and z0= -2.33

The standardized test statistic

Standard error of the mean = 6237/sqrt(70) = 745.46

z= (125070 - 127000)/745.46 = -2.59

As, standardized test statistic (-2.59) < critical value (-2.33), the standardized test statistic is in the rejection region and we can reject H0.

So, in case of (B) Use the same values, but increase alpha± from 0.01 to 0.05 and (D) Use the same values, but increase n from 35 to 70, we can reject H0.

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