Question

write out all the steps of hypothesis testing including populations, hypotheses, cutoff scores, and all relevant calculations.

Nationwide survey in 92' showed US middle school students spend u=8.4 hours doing homework. Distribution is normal o=3.2. Previous year 100 middle school students and the mean of their homework time was 7.1. Was there a significant change in homework times.Test through a=.05

A student thinks he can reduce the time spent in institutions for people with severe depression. A director lets him try on 20 cases randomly sampled from the institution. The mean stay is 85 weeks with a standard deviation of 15 weeks. Scores are normally distributed. He bumped the stay of these patients to 78 weeks. What can be concluded from the study. Use a=.05

Answer 1

1)
Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 8.4
Alternative Hypothesis: μ ≠ 8.4

Rejection Region
This is two tailed test, for α = 0.05
Critical value of z are -1.96 and 1.96.
Hence reject H0 if z < -1.96 or z > 1.96

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (7.1 - 8.4)/(3.2/sqrt(100))
z = -4.06

P-value Approach
P-value = 0
As P-value < 0.05, reject the null hypothesis.

2)
Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 78
Alternative Hypothesis: μ ≠ 78

Rejection Region
This is two tailed test, for α = 0.05 and df = 19
Critical value of t are -2.093 and 2.093.
Hence reject H0 if t < -2.093 or t > 2.093

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (85 - 78)/(15/sqrt(20))
t = 2.087

P-value Approach
P-value = 0.051
As P-value >= 0.05, fail to reject null hypothesis.