Question

Austin Clemens is writing a report for his high school environmental science class about the city’s climate. To impress his teacher, Austin would like to show evidence that the population mean daily low temperature during the five-year period from 1998–2002 is less than the population mean daily low temperature during the five-year period from 2013–2017. He researches the claim using a website that records all of the weather data observed at a local airport. After conducting the research, Austin assumes that the population standard deviation is 10.48∘F for 1998–2002 and 11.29∘F for 2013–2017. Due to the large amount of data in each five-year period, Austin randomly selects the daily low temperatures for each group. The sample statistics are shown in the table below. Let μ1 be the population mean daily low temperature during the five-year period from 1998–2002 and μ2 be the population mean daily low temperature during the five-year period from 2013–2017. The p-value rounded to three decimal places is 0.192, the significance level is α=0.10, the null hypothesis is H0:μ1−μ2=0, and the alternative hypothesis is Ha:μ1−μ2<0.

1998–2002 2013–2017 x

x=44.31∘F x2=46.02

n=59 n=63

Which of the following statements are accurate for this hypothesis test to evaluate the claim that the difference between the population mean daily low temperature during the five-year period from 1998–2002 and the population mean daily low temperature during the five-year period from 2013-2017 is less than zero? Select all that apply:

A)Reject the null hypothesis that the true difference between the population mean daily low temperature during the five-year period from 1998–2002 and the population mean daily low temperature during the five-year period from 2013-2017 is equal to zero.

B)Fail to reject the null hypothesis that the true difference between the population mean daily low temperature during the five-year period from 1998–2002 and the population mean daily low temperature during the five-year period from 2013-2017 is equal to zero.

C)Based on the results of the hypothesis test, there is not enough evidence at the α=0.10 level of significance to suggest that the true difference between the population mean daily low temperature during the five-year period from 1998–2002 and the population mean daily low temperature during the five-year period from 2013-2017 is less than zero.

D)Based on the results of the hypothesis test, there is enough evidence at the α=0.10 level of significance to suggest that the true difference between the population mean daily low temperature during the five-year period from 1998–2002 and the population mean daily low temperature during the five-year period from 2013-2017 is less than zero.

Answer 1

The Decision rule is that if p value is < , Then reject The null Hypothesis.

In this case, p value (0.192) is > (0.10), so we would fail to reject the null hypothesis.

The Null hypothesis is the the population mean temperatures in the period 1998 - 2002 () is equal to population mean temperatures in the period 2013 - 2017 () and the claim is the alternative hypothesis that this difference is less than 0.

Therefore the conclusion must address the claim.

Therefore Option C: Based on the results of the hypothesis test, there is not enough evidence at the = 0.10 level that the true difference between the population mean daily low temperature during the 5 year period from 1998 - 2002 and the population mean daily low temperature during the 5 year period from 2013 - 2017 is less than zero.