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Question 846:



No answer provided yet.We can use the 1-sample t-test to test the sample mean against the test criteria of 6 percent. We use the 1-sample t-test and not the 2-sample t-test because we are comparing a sample of data to a benchmark (6 percent). We would use a 2-sample t-test if there were to sample's we needed to compare.

The Null Hypothesis is that the mean 30-year mortgage rate is less than or equal to 6 percent. The alternative hypothesis is that the mean rate is greater than 6 percent. We will reject the Null Hypothesis if the p-value is less than the alpha cut-off value of .01.

Since we do not know the population standard deviation and the sample size is small (less than 30) we will use the 1-sample t-test instead of the 1-sample z-test. The test statistic t, is found as the difference between the sample mean and test mean. The sample mean is 5.6375 (6-5.6375) = .3625 percent. We divide this difference by the standard error of the mean (SE). The SE is found as the standard deviation divided by the square root of the sample size = .635/SQRT(8) = .224. The test statistic t = .3625/.224 = 1.62

The one-sided p-value associated with this t-score can be found using a t-table on 7 degrees of freedom (8-1). You can also use the excel excel function =TDIST(1.62, 7,1) and we get the one-sided p-value of .075.

Since the p-value is above the alpha cutoff of .05 we cannot reject the Null Hypothesis. We can conclude there is sufficient evidence given the sample of 8 mortgage rates to agree with the article that the mortgage rate is less than 6 percent. 

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