Question

Suppose that you are testing the following hypotheses: Ho: = 10 and 11: > 10. If the null hypothesis is rejected at the 1% level of significance, what statement can you make about the confidence interval on the mean? a) The lower bound of a 95% one-sided confidence interval on the mean exceeds 10. b) 9 sus 13 c) No statement can be made. d) The lower bound of a 95% one-sided confidence interval on the mean exceeds zero. If we know the population standard deviation and we use the t-test instead of the Z-test, a) We will increase the probability of type II error. b) We will increase the probability of type I error. c) We will have the same conclusion d) None of the above The chi-square goodness-of-fit test can be used to test for: a) significance of sample statistics b) difference between population means c) normality d) probability What is the purpose of a goodness-of-fit test? a) To assess whether there is a significant difference between a collection of categorical data b) To find relationships in the data c) To assess whether several categorical variables are related d) To assesses whether the central tendency, variability and distribution of sample is different from that of the population Suppose you are testing the following hypothesis pair: Ho:4 s 100 vs. Hy :u > 100. A sample average of less than 100 would sometimes lead to a error but would never lead to a error. a) Type I; Type II b) Type II; Type I c) Type II; p-value d) p-value; Type II

Answer 1

1.

If the null hypothesis is rejected, then the confidence interval will not contain the value 10.

Also since alternative hypothesis is μ > 10 , the lower bound of the confidence interval will exceed 10.

Also here, we test at 1% level. The confidence interval at 95% is wider than a 99% confidence interval.

So, we cannot make any claims regarding 95% interval with a 1% level of significance test.

So, answer is :

c) No statement can be made

2.

Z test uses the population standard error and t test uses the estimated standard error. So Z test is more powerful than t test.

So, if we use t test instead of Z test, the power of the test decreases.

Also, Power = 1 - P ( Type 2 error )

So, if we use t test instead of Z test, probability of Type 2 error increases

So, answer is :

a) We will increase the probability of type 2 error

3.

Chi-Square goodness of fit test is used to compare the observed sample distribution with the expected probability distribution. It tests how well a sample fits to a theoretical distribution.

So it can be used to test for normality.

So, answer is :

c) Normality

4.

The goodness of fit of a sample shows how well it fits to a theoretical model or distribution.

So, answer is :

d) To assess whether the central tendency, variability and distribution of sample is different from that of the population.

5.

Type 1 error is rejecting null hypothesis when it is true.

Type 2 error is non rejection of null hypothesis when it is false.

Here, if sample average is less than 100, it would sometimes lead to rejection of null hypothesis when it is true but never lead to non rejection of null hypothesis when it is false.

So answer is :

a) Type 1; Type 2