Question

The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude, and study habits of college students. Scores range from 0 to 200 and follow (approximately) a Normal distribution with a mean of 115 and a standard deviation of 25. You suspect that incoming freshmen at your school have a mean μ, which is different from 115 because they are often excited yet anxious about entering college. To test your suspicion, you decide to test the hypotheses H0: μ = 115 versus Ha: μ ≠ 115. You give the SSHA to 25 incoming freshmen and find their mean score to be 116.2. What is the value of the test statistic?
A) z = 0.048
B) z = 0.24
C) z = 1.2
D) z = 1.96

Answer 1

Answer:

option B

Step-by-step explanation:

hypothesis test:

H₀ : μ = 115

Ha: μ ≠ 115

This is two tailed test

$\bar{x} = 116.2$

$\sigma = 25$

n = 25

significance level = ∝ = 0.05

$Z =\dfrac{\bar{x} -\mu}{\dfrac{\sigma}{\sqrt{n}}}$

$Z =\dfrac{116.2 - 115 }{\dfrac{25}{\sqrt{25}}}$

$Z =\dfrac{116.2 - 115 }{\dfrac{25}{5}}$

$Z =\dfrac{1.2}{5}$

Z = 0.24

the correct answer is option B