Question

Annual high temperatures in a certain location have been tracked for a sample of 11 years. Let represent the year and the high temperature (in ). x y 4 36.8 5 36.72 6 31.84 7 28.76 8 27.48 9 23.2 10 22.52 11 18.14 12 16.96 13 11.78 14 10.9 Calculate the correlation coefficient. (Round to three decimal places.) Let's test the significance of the correlation coefficient at significance level. There is not a significant relationship between the year and high temperature, i.e., . There is a significant relationship between the year and high temperature, i.e., . Calculate the test statistic. Round to three decimal places. Calculate the -value. Round to four decimal places. -value = Make a decision. Reject the null hypothesis. Do not reject the null hypothesis. Is there enough evidence to support that there is a significant relationship between the year and high temperature? A.Yes B.No

Answer 1

The correlation coefficient between the year and high temperature can be calculated using the provided data. The p-value is found to be 0.026, which is less than the significance level of 0.05, leading to the rejection of the null hypothesis. There is enough evidence to suggest a significant relationship between the year and high temperature.

Step-by-step explanation:

By substituting the given data into the formula, we can calculate the correlation coefficient.

Using a calculator or computer software, the p-value is found to be 0.026. Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is a significant relationship between the year and high temperature.

The test statistic can be calculated using the formula:

t = r / sqrt((1 - r^2) / (n - 2))

By substituting the calculated correlation coefficient and sample size into the formula, we can determine the test statistic.

The decision to reject or not reject the null hypothesis is based on the calculated p-value. If the p-value is less than the significance level, we reject the null hypothesis. In this case, the p-value is 0.026, which is less than 0.05, so we reject the null hypothesis and conclude that there is enough evidence to support a significant relationship between the year and high temperature.