Harold wants to check with an appropriate hypothesis test whether the substance works, i.e. whether the substance reduces leakage. Halli is a promising statistician and realizes that it is appropriate to perform a bilateral test. What is the value of the test size? 1.771. 2,340. 1.960 3.176       What is the rejection area in Halla's hypothesis test? (remember that Halli performs a two-way test). t <−2.776 and t> 2.776. t <−2.306 and t> 2.306. t <−2.262 and t> 2.262. t <−1.96ogt> 1.96.   Each of the statements below is correct based on the results of the hypothesis test. haroldshould reject the null hypothesis and conclude that the material reduces leakage. harold should reject the null hypothesis and conclude that the material does not work. harold should accept the null hypothesis and conclude that the material does not work. None of the above statements is correct.

Harold is going to California over the Easter weekend and takes part in the Rock Festival of the people. He is an optimistic man and intends to sleep in a tent. He is worried about leaks in the tent, but to his great satisfaction, he came across an advertisement for material that the manufacturers claim reduces leakage in tents by spraying it on the outer layer of the tent. He was not convinced but found a study where the material was examined. In the study, leakage in five tents was measured. First, it was measured how much it leaked without the material too much and then how much it leaked after the material was sprayed on the outer layer in each tent. High numbers mean high leakage and low numbers low leakage. It can be assumed that measured leaks follow a normal distribution. The results can be seen below:

Harold is also a big fan of R and he performed the following calculations in R:

> x<-c(8.6,9.2,7.8,7.2,8.9) > y<-c(6.2,7.2,7.6,8.2,6.1) > mean(x)
[1] 8.34

> mean(y)
[1] 7.06
> sd(x)
[1] 0.8234076 > sd(y)

[1] 0.9044335 > d<-x-y
> mean(d)
[1] 1.28

> sd(d)
[1] 1.616168

Questions 1 – 3 deal with harold and his experiment.

1. Harold wants to check with an appropriate hypothesis test whether the substance works, i.e. whether the substance reduces leakage. Halli is a promising statistician and realizes that it is appropriate to perform a bilateral test. What is the value of the test size?
2. 1.771.
3. 2,340.
4. 1.960
5. 3.176

1. What is the rejection area in Halla's hypothesis test? (remember that Halli performs a two-way test).
2. t <−2.776 and t> 2.776.
3. t <−2.306 and t> 2.306.
4. t <−2.262 and t> 2.262.
5. t <−1.96ogt> 1.96.

1. Each of the statements below is correct based on the results of the hypothesis test.
2. haroldshould reject the null hypothesis and conclude that the material reduces leakage.
3. harold should reject the null hypothesis and conclude that the material does not work.
4. harold should accept the null hypothesis and conclude that the material does not work.
5. None of the above statements is correct.