Please solve these questions and why we choose the answers. Thanks! 6. Suppose a
ID: 3354342 • Letter: P
Question
Please solve these questions and why we choose the answers. Thanks!6. Suppose a study was done to determine if the average amount of sleep that students get the day before an exam is less than 6 hours. An SRS of 100 students from a university was taken and a mean of 5.5 hours was computed from the sample. The figure below provides the results of the analysis. Density 0.4 0.3 0.2 0.1 .3 .2 -1 The alternative hypothesis is A) one-sided B) two-sided C) three-sided D) four-sided 7. When we state the alternative hypothesis to look for a difference in a parameter in any direction, we are doing a A) one-sided test B) two-sided test C) None of the above 8. The the P-value, the stronger the evidence against the null hypothesis provided by the data. A) larger B) smaller 9. Given that a test of significance was done for a two-sided test and the P-value obtained was 0.02, what would be the P-value for a one-sided significance test? A) 0.02 B) 0.04 C) 0.01 D) 0
Explanation / Answer
6) We want to test the avarage amount of sleep that student get the day before an exam is less than 6 hours.
Suppose mu = avarage amount of sleep that student get the day before an exam.
i.e. We want to test the hypothesis
Ho : mu =6 against H1 : mu < 6 ( Left-tailed one sided )
alternative hypothesis : H1 : mu < 6
correct answer : one-sided
7) suppose the alternative hypothesis to look for a difference in a parameter in any direction.
in this case the alternative hypothesis
H1 : mu # muo ( i.e. mu > muo or mu < muo ) we look the difference in both the direction.
where muo is the value of population parameter under the null hypothesis
Correct answer : two-sided test
8) If the p-value is less than level of significance level aplha that suggests that the observed data is sufficiently inconsistent with the null hypothesis and we reject the null hypothesis.
i.e. if the p-value is small then there will be strong evidence to reject the null hypothesis.
Correct answer : smaller
9) suppose p is p-value for one-side test, then for two-sided test p-value is
p-value = 2 *p.
Here p-value for two-sided test is given by 0.02
Hence for one-sided test p-value is given by p-value = 0.02/2 = 0.01
Correct answer : 0.01