Homework #4 Name ______________________________

Chapter 8

1. When conducting statistical analyses, we are always formally testing the null hypothesis. Why can we never accept the null hypothesis as being true? (½ pt)

 

 

 

2. a. what is a Type I error? (½ pt)

2. what is a Type II error? (½ pt)

 

 

3. what is an alpha level? (½ pt)

 

 

4. how are these three things related? (1 pt)

1. Under what circumstances do we conduct a t-test instead of a z-test? (1 pt)

 

 

2. A researcher administered a test of verbal ability to a sample of 169 students. The mean of the sample was 74.40. The standard deviation for the population, s , was known to be 13.00. Compute the 95% confidence intervals. (1 pt)

 

 

 

 

 

4b. Calculate the 95% confidence intervals for the true population mean if the above test population was known to have a standard deviation of 7.0: (1pt)

 

 

 

 

4c. What is effect of decreasing s on the width of the confidence intervals? (½ pt)

3. You are interested in how well people can estimate the passage of time without the aid of a time-telling device. To test this, you ask 25 people to tell you when they think a 7-minute interval has passed without using a watch or clock. The mean of these 25 estimates was 6.25 minutes, with a standard deviation estimate of 1.75 minutes. Use a non-directional one-sample t-test to determine whether your sample mean came from a population with a mean of 7 minutes?

1. State your formal hypotheses: (¼ pt)

 

2. What are your degrees of freedom? What are your critical values? (½ pt)

 

3. Calculate the estimated standard error of the mean: (1 pt)

 

 

4. Calculate t_obs: (1 pt)

 

 

5. What is your decision? (¼ pt)

 

 

6. Calculate the 95% confidence intervals: (1 pt)

1. For each of the following t_obs values, use the df (in parentheses) to determine the critical values and indicate your decision regarding the H_O: (2 ½ pts)

1. t_obs(5) = +3.014
2. t_obs(19) = -1.989
3. t_obs(16) = -2.179
4. t_obs(30) = +2.036
5. t_obs(13) = +2.262