Question

The mean score on a science assessment for 59 male high school students was 319.5 and the standard deviation 2.5. The mean test score on the same test for 40 female high school students was 298.9 and the standard deviation was 1.2. For this assessment, the population standard deviation for males is σ = 2.3 and the population standard deviation for females is σ = 2.0. At a =. 02 , can you support the claim that mean scores on the science assessment for male high school students were higher than for the female high school students?

Answer: a. Claim:


Ho:

Ha:

b. LTT, RTT or TTT ?


c. Hypothesis testing to use:


Why?





d. Standardized test statistic (formula and value)



e. P-value



f. Decision:




g. Interpretation: At  

Answer 1

Solution:

a. Claim: . The mean scores on the science assessment for male high school students were higher than for the female high school students.

b. RTT (right-tailed test)

c. Hypothesis testing to use:
Answer: The hypothesis testing to use is the two-sample z-test

Why?

Because the population standard deviations are known

d. Standardized test statistic (formula and value)

  

  

e. P-value

Using the standard normal distribution, we have:

f. Decision:
Answer: Since the p-value is less than the significance level 0.02, we, therefore, reject the null hypothesis

g. Interpretation: At significance level, there is sufficient evidence to support the claim that mean scores on the science assessment for male high school students were higher than for the female high school students