Selling prices for 230 diamonds evaluated by two different diamond ratings agenc

Question

Selling prices for 230 diamonds evaluated by two different diamond ratings agencies (GIA and HRD) were collected and the data was analyzed using the Microsoft Excel Data Anlaysis Toolpak. The following results were generated in Excel inputting alpha .05 in the Excel dialog box. Based on the Microsoft Excel Data Analysis results, if the the hypothesis test is testing "whether the mean retail sales price of GIA is less than the mean retail sales price of HRD:" the conclusion of this hypothesis test based on a .05 level of significance: is: A. Since the decision rule is if z-test statistic 1.645, the test statistic -4.46 indicates e null hypothesis should not be rejected at the .05 level of significance, indicating there is not sufficient evidence to suggest the mean retail selling price of GLA is less than the mean retail selling price of HRD.

Explanation / Answer

Solution:

Option

Topic:Hypothseis Testing

Define nUll and alterrnate hypotheisis:

Null hypothesis:

H0:No change in mean retail sales price of GLA and HRD

ALternate Hypothesis:

Ha:the mean retail sales price of GIA< mean retail sales price of HRD

SInce sample size large >30

we go for Normal distribution(Z test)

Test statistic obtained isZ=-4.46(2 decimals)

Level of significance=0.05

Confidence level=1-.05=0.95=95%

Z critical for 95% confidence level is -1.96

Statistical Decision:

Since Z(calculated)=-4.46

less than Z (critical)=-1.96

and falls in the Rejection region, we will Reject the null hypothesis

Rejecct Null Hypothesis.

Accept Alternate Hypotheisis

We can statistically conclude that the mean retail sales price of GIA< mean retail sales price of HRD

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