What is the value of the corresponding p-value?

1.Fill in the blank. If the response is quantitative and modeled by some unknown density function, hypothesis tests about the center of the density use the                                           .
(a) mean
(b)variance
(c) median
(d) standard deviation

2.Fill in the blank. In the analysis of paired data, the paired T-test is used if the differences between pairs can be modeled by a normal distribution. If the normal distribution is not an appropriate model, the                                           can be used instead.
(a)sign test
(b)rank sum test
(c)signed rank test
(d)Kruskal-Wallis test

3.Fill in the blank. In the analysis of two independent samples, the two-sample T-test is used if the normal distribution is an appropriate model for both populations. If the normal distribution is not an appropriate model, the                                           can be used instead.
(a)sign test
(b)rank sum test
(c)signed rank test
(d)Kruskal-Wallis test

4.True or false for the sign test: A large value of R supports the alternative hypothesis
H₁: π_.5 > π_.5⁰.
(a)True
(b)False

5.True or false for the sign test: Under the null hypothesis, the distribution of R depends on the value of the hypothesized median.
(a)True
(b)False

6.Fill in the blank. For the signed rank test, the distribution of the test statistic W⁺ (under the null hypothesis of no difference) depends on                                                        
(a)the sample size
(b)the number of positive differences
(c)the number of non-zero differences

7.True or false for the Kruskal Wallis test: Under the null hypothesis that the distributions for the I populations are all the same, the distribution of the test statistic is approximately chi-squared with I degrees of freedom.
(a)True
(b)False

Questions 8 through 12 are based on the following scenario.

A contractor is building houses right outside of the city. He is trying to make these houses affordable for low-income families. In a certain housing development he is building a large number of houses of about the same size and value. The contractor claims that the median price for these houses is below $100,000. Six houses were selected at random and their value assessed by a real estate appraiser. The values were:

95,500102,00098,00096,50093,00097,500

8.State the hypotheses to test if the true median price is equal to $100,000 or if it is less than $100,000 as the contractor claimed.

1.                 What is the distribution of the test statistic R under the null hypothesis?

1.             What is the value of the observed test statistic?

1.             What is the value of the corresponding p-value?
   
2.             At a significance level of 10%, do we reject H₀?
   (a)              Yes
   (b)              No