Question

Please label and show each step

3. A sample of 100 high school students was provided a special training program designed to improve their speed reading skills. A month after the conclusion of the course, the students were contacted and asked whether the skills learned in the program were effective. 60 responded YES.

1. State the null and alternative hypothesis such that one may conclude that if the null hypothesis is rejected then the program was effective.

2. State the test statistic you will use.

3. State your decision rule (use a level of significance of 0.1)

4. What is the value of your test statistic?

5. What can you conclude?

Answer 1

There are two population one before the special training and one after the training

a.

Null Hypothesis: There is no difference between the two means.

Alternate Hypothesis: There is a difference between the two means.

H₀: mu₁ = mu₂

H₁: mu₁ =/=  mu₂

b. The test static that will be used is t-test.

c. t observed = (mu - Xbar)/ standard error

• Mu= population mean
• X bar= Sample mean
• standard error = Standard deviation of sample/ Square root of n
• n= sample size

t critical value = T.INV.2T(aplha=0.01, degrees of freedom= n-1) [ excel function]

d. and e. If t observed < t critical , then t observed lies in acceptance region and we fail to reject Ho.

Please note: Many values are missing from the question, but the above steps can be followed to arrive at the decision provided all the other information.