calculate a confidence interval for the true mean of the population of all home sales prices for this town. 1. In one to two complete

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Using the home sales prices data attached, calculate a confidence interval for the true mean of the population of all home sales prices for this town.

1. In one to two complete sentences, explain what this confidence interval means for this particular study. State clearly, using the meaning of the confidence interval in terms of the words and context of the problem described.

2. What happens to the EBM as the confidence level increases? Does the width of the confidence interval increase or decrease? Explain why.

Expert Solution
Step 1

From the sales price data,

The sample size is, n=20

The sample mean is,

Statistics homework question answer, step 1, image 1

The sample standard deviation is,

 

Statistics homework question answer, step 1, image 2

Step 2

2)

Let Statistics homework question answer, step 2, image 1denote the average sales of a price of home.

The average price of home in 2008 was $390,000

The mayor's claim is that the average sales of a price of home is not less than the average precession price in 2008.

The null hypothesis is that the average sales of a price of home is not less than the average precession price in 2008.

Statistics homework question answer, step 2, image 2

The alternative hypothesis is the average sales of a price of home is  less than the average precession price in 2008.

Statistics homework question answer, step 2, image 3

The test statistic is,

Statistics homework question answer, step 2, image 4

The level of significance is,

Statistics homework question answer, step 2, image 5

From the alternative hypothesis it is clear that the test is right tailed test.

The degrees of freedom is,

Df= n-1=20-1=19

From t table at 0.10 level of  significance with 19 degrees of freedom, the right tailed critical value is,

Statistics homework question answer, step 2, image 6

Decision rule:

Reject the null hypothesis if 

Statistics homework question answer, step 2, image 7

Computation of p value:

Statistics homework question answer, step 2, image 8

Decision :

Reject the null hypothesis if p value is less than the level of significance.

Here, p value is 0.9096 which is greater than 0.10 . so fail to reject the null hypothesis and conclude that the average sales of a price of home is not less than the average precession price in 2008.

 

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