A. (H₀): The average Math ACT score ≤ 23
(Hₐ): The average Math ACT score ≥ 23
B. Test statistic is 5.65 and the p-value is < .00001 Therefore reject the H₀.
C. There is sufficient evidence to suggest that the average Math ACT score for freshman at community colleges is greater than 23.
How do we test the hypothesis?
To test the claim that the average Math ACT score for freshman at community colleges is greater than 23.
we say
A. Null Hypothesis (H₀): The average Math ACT score for freshman at community colleges is equal to or less than 23.
Alternative Hypothesis (Hₐ): The average Math ACT score for freshman at community colleges is greater than 23.
A random sample of 150 community college students was conducted. The results were x = 23.6 and s = 1.3. Use a significance level of 0.10.
B. Calculate the t-statistic
t = (Xbar - μ) / (s / √n)
t = (23.6 - 23) / (1.3 / √150)
t ≈ 5.65
t-distribution table with 149 degrees of freedom (df = n - 1) and a one-tailed test at 0.10 significance level, the p-value is < .00001. We reject the null hypothesis
C. The t-statistic of approximately 5.65 falls into the critical region, and the p-value is very small, indicating strong evidence against the null hypothesis.