Question

Suppose the school superintendent of Metro County wants to know if the mean score on the ninth-grade Biology final for students in her county is different from the state mean. She knows the state scores on the Biology final follow a normal distribution and the state mean is 115.2 points. The superintendent decides to conduct a one-sample t ‑test for a mean. She obtains the following results, based on a simple random sample of 700 students in her county.

Sample size Sample mean Sample standard Test statistic Probability value
deviation
n xbar s t p‑value
755 115.57 5.28 points 1.93 0.055.
Determine if the results are statistically significant at the 0.10 significance level. The results_______statistically significant at the 0.10 level because p_________0.10.

Answer 1

The results are statistically significant at the 0.10 level because p (given in the question) is less than 0.10.

Explanation:

The given details are as below:

μ = 115.2

n =755

x-bar =115.57

s = 5.28 points

t = 1.93

p‑value = 0.055

We have to test whether H₀ : μ = 115.2

H₁: μ ≠ 115.2

At α =0.10 level.

The results are statistically significant at the 0.10 level because p (given in the question) is less than 0.10.