Question

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

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

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.

#### Earn Coins

Coins can be redeemed for fabulous gifts.