Question

A recent article claimed that the mean wedding cost in the US is $28,400. A random sample of 44 weddings from this year was taken from the western New York region. Test, at the 5% significance level, if the mean cost of a wedding in Western New York is different than the national average.

The costs of those weddings are in the Excel spreadsheet under the Files link, in the tab named Wedding costs.

What is the value of the test statistic? (round to four (4) decimal places)

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Question 21 pts

What is the p-value for this hypothesis test? (Use four (4) decimal places)

Question 31 pts

What is the size of effect for this hypothesis test? (round to two (2) decimal places)

Question 41 pts

In reference to the previous question, answer the following:

What is the decision?

                           [ Select ]                       ["Since the p-value is more than the significance level, we reject the null hypothesis", "Since the p-value is less than or equal to the significance level, we fail to reject the null hypothesis", "Since the p-value is larger than the significance level, we fail to reject the null hypothesis", "Since the p-value is less than or equal the significance level, we reject the null hypothesis"]      

From the possible conclusions, choose the correct statement from below:

                           [ Select ]                       ["At the 5% significance level, there is sufficient evidence to conclude that the mean cost of weddings in Western New York is equal to the national mean cost of $28,400.", "At the 5% significance level, there is not sufficient evidence to conclude that the mean cost of weddings in western New York is different than the national mean cost of $28,400.", "At the 5% significance level, there is sufficient evidence to conclude that the mean cost of weddings in western New york is different than the national mean of $28,400"]      

Choose the correct statement regarding the type of error that may have been committed in this hypothesis test.

Data

18600

19100

34600

36900

30900

28700

34700

29200

1500

51700

40400

34000

29100

32700

11600

21700

37000

31400

2200

1300

14700

34000

16700

12100

33900

29100

25100

44800

44700

40700

16600

22000

44700

28100

31100

35100

43800

13200

25600

28700

8000

46400

26900

9700

Answer 1

We do not know population standard deviation (or variance). So we have to perform t-test.

We have to test for null hypothesis

against the alternative hypothesis

Our test statistic is given by

where

So, the value of test statistic is -0.5507.

Degrees of freedom

P-value = 0.5846943 [Using R-code 'pt(-0.5506927,43)+1-pt(0.5506927,43)']

So, p-value for the hypothesis test is 0.5847

Size of the hypothesis test is

We reject null hypothesis if

Here, we see and so we cannot reject our null hypothesis.

So, our decision is as follows.

Since the p-value is larger than the significance level, we fail to reject the null hypothesis.

So, our conclusion is as follows.

At the 5% significance level, there is not sufficient evidence to conclude that the mean cost of weddings in western New York is different than the national mean cost of $28,400.