Question

The z statistic for a one-sided test is z* = 2.327. This test is

• A. not significant at α = .005 but significant at α = .01 level
• B. significant at α = .005 but not at α = .01 level
• C. significant at all levels
• D. not significant at either α = .005 nor α = .01 level
• E. not significant at all levels
• F. significant at both α = .005 and α = .01 level

An experiment was done on how long it takes students to navigate through a nearby corn maze at night. The mean time was 32 minutes. A researcher thinks giving students a flash light will help them complete the maze faster. A sample of 10 students who were given a flash light had a sample mean of x-bar = 29.5 minutes. The null hypothesis for the significance test would be

• A. H_o: μ = 32
• B. H_o: μ < 32
• C. H_o: μ > 32
• D. H_o: μ ≠ 32
• E. H_o: μ = 29.5
• F. H_o: μ <; 29.5
• G. H_o: μ > 29.5
• H. H_o: μ ≠ 29.5

The alternative hypothesis for the problem is

• A. H_a: μ = 32
• B. H_a: μ < 32
• C. H_a: μ > 32
• D. H_a: μ ≠ 32
• E. H_a: μ= 29.5
• F. H_a: μ < 29.5
• G. H_a: μ > 29.5
• H. H_a: μ ≠ 29

Answer 1

Solution:

1)

One tailed test

p value = P(Z > +2.327) = 1 - P(Z < +2.327) = 1- 0.9900 = 0.0100

When p value is $\leq$   $\alpha$ , then we reject H0 and test is said to be significant.

not significant at α = .005 but significant at α = .01 level

2)

The null hypothesis is

H_o: μ = 32

3)

The alternative hypothesis is

H_a: μ < 32