Question

A researcher is investigating the effects of a new studying program for high school students hoping to increase test scores on the ACT exam. The ACT has a population average of 21.1 and standard deviation of 3.2 for the composite score. The researcher had 15 participants in the study who had an average ACT composite score of 23.3. Use a .035 level of significance.

Name the null and alternative hypotheses (1 point)

What is the critical value to test this at the .035 level (1 point)?

What is the value of the test statistic (2 points)?

What decision should the researcher make (1 point)?

Answer 1

Solution :

= 21.1

= 23.3

= 3.2

n = 15

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   = 21.1

H_a : >  21.1

The significance level is α = 0.035

The critical value for a right-tailed test is t_c​=1.962.

Test statistic = z

= ( - ) / / n

= (23.3-21.1) /3.2 / 15

= 2.663

p(Z >2.663 ) = 1-P (Z <2.663 ) = 0.0093

P-value = 0.0093

= 0.035

p=0.0093<0.035, it is concluded that the null hypothesis is rejected.

There is enough evidence to claim that the population mean μ is greater than 21.1, at the 0.035 significance level.