Question

1. Which of the folloiwng statements are true
   1. A sample t test is used to test the differences between a sample mean and a population mean to determin statistical significance
   2. One sample t test is used to test the difference between two sample means from one sample
2. SAT verbal scores are normally distributed with the population mean of. An 500. A local high school has instituted a new program to engage students in reading. A sample 90 students from this high school is randomly selected following their participation in this reading program and their SAT verbal score mean of 520 was compared to the national mean. Discuss how this would require a One Sample t Test.
3. For the above example, how would you set up a two-tailed alternative hypothesis and what would you conclude whether the null hypothesis was rejected.
4. How would you set up a one-tailed alternative hypothesis for the above example and what would you conclude if the null hypothesis was rejected.
5. Assume that one sample t Test showed the following results (t(49) = 21, p < .01). Answer the following questions.
   1. What is the probability that the null hypothesis is true?
   2. What is the df of the study
   3. What is the n of the study

What would you conclude

Answer 1

a.

True - A sample t test is used to test the differences between a sample mean and a population mean to determin statistical significance

b.

False - Two sample t test is used to test the difference between two sample means from one sample

Since we do not know the population standard deviation of the students score, we will use one sample t test.

Two-tailed alternative hypothesis is,

Ha: Mean SAT verbal score after the program is not equal to 500.

If the null hypothesis is rejected, we conclude that there is significant evidence that Mean SAT verbal score after the program is not equal to 500.

One-tailed alternative hypothesis is,

Ha: Mean SAT verbal score after the program is greater than 500.

If the null hypothesis is rejected, we conclude that there is significant evidence that Mean SAT verbal score after the program is greater than 500.

a.

(t(49) = 21, p < .01).

Probability that the null hypothesis is true is less than 0.01

b.

df of the study is 49.

c.

n of the study is df + 1 = 49 + 1 = 50

d.

Since p-value is less than 0.01 significance level, we reject null hypothesis H0 and conclude that there is significant evidence that the alternative hypothesis is true.