Question

1) Use the normal distribution and the sample results to complete the test of the
hypotheses. Use a 5% significance level. Assume the results come from a
random sample.
a) Test ?!: ? = 15 ?? ?!: ? > 15 using the sample results ? = 17.2 , ? =
6.4 with ? = 40
b) Test ?!: ? = 100 ?? ?!: ? < 100 using the sample results ? = 91.7 , ? =
12.5 with ? = 30
c) Test ?!: ? = 500 ?? ?!: ? ≠ 500 using the sample results ? = 432 , ? =
118 with ? = 75

2) Use the Student-t distribution and the sample results to complete the test of
the hypotheses. Use a 5% significance level. Assume the results come from a
random sample, and if the sample size small, assume the underlying
distribution is relatively small.
a) Test ?!: ? = 10 ?? ?!: ? > 10 using the sample results ? = 13.2 , ? =
8.7 with ? = 12
b) Test ?!: ? = 120 ?? ?!: ? < 120 using the sample results ? = 112.3 , ? =
18.4 with ? = 100
c) Test ?!: ? = 4 ?? ?!: ? ≠ 4 using the sample results ? = 4.8 , ? = 2.3 with
? = 15

3) A t-test for a mean uses a sample of 15 observations. Find the t-test statistic
value that has a P-value of 0.05 when the alternative hypothesis is
a) ?!: ? ≠ 0
b) ?!: ? > 0
c) ?!: ? < 0

4) A study has a random sample of 20 subjects. The t-test statistic for testing
?!: ? = 100 is ? = 2.40. Find the approximate P-vale for alternative
a) ?!: ? ≠ 100
b) ?!: ? > 100
c) ?!: ? < 100

Answer 1