The cost of a one-carat VS2 clarity. H color diamond from Diamond Source USA is

Question

The cost of a one-carat VS2 clarity. H color diamond from Diamond Source USA is $5600. A midwestern jeweler makes calls to contacs in the diamond district of New York City to see whether the mean price of diamonds there differs from $5600.

a. Formulate hypothesis that can be used to determine whether the mean price in New York city differs from $5600.

b. A sample of 25 New York contacts provided the prices shown in the CD file named Diamonds. What is the p-value?

c. At a=.05 can the null hypothesis be rejected? What is your conclusion?

d. Repeat the preceding hypothesis test using the critical value approach.

I am not sure what information is missing but don't use excel.

Explanation / Answer

Solution:-

The solution to this problem takes four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. We work through those steps below:

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: = 5600
Alternative hypothesis: 5600

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample mean is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the z-value and degrees of freedom (DF).

Critical value of z, for the significance level of 0.05, is

zc = -1.96 and zc = 1.96

Degree of freedom = n - 1 = 25 -1 = 24

After calculating the value of z above, then we use the z Distribution Calculator to find P-value(which is available online).

The P-Value is 0.049996.
The result is significant at p < 0.05.

Interpret results. Since the P-value is smaller than the significance level (0.05), we can reject the null hypothesis. That is the mean value may differ from $5600.

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