Question

1) If a hypothesis is conducted using 𝐠= 0.05, for which of the following p-values would the null hypothesis be rejected?

2) For each pair of ? and p-value, indicate whether the null hypothesis would be rejected.

3) In a test of H₀: µ = 80 against H₁: µ＜80, the sample data yielded the test statistic z = 1.63. What is

the p-value for the test?

4) In a test of H₀: µ = 80 against H₁: µ ≠ 80, a sample of observations had a mean and standard

deviation s = 4.1. What is the p-value for this test?

5) In a test of H₀: µ = 72 against H₁: µ ≠ 72, the sample data yielded the test statistic z = 1.63. Find the p-value for the test.

Answer 1

1)

e) 0.001

2)

a) $p=0.10>0.05=\alpha,$ don't reject

b) $p=0.05=0.05=\alpha,$ don't reject

c) $p=0.001<0.01=\alpha,$ reject

d) $p=0.10>0.01=\alpha,$ don't reject

e) $p=0.01<0.10=\alpha,$ reject

3)

Left-tailed test $p=P(Z<1.63)=0.948449$

4)

This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation, using the sample standard deviation, will be used.

The t-statistic is computed as follows:

$$t=\dfrac{\bar{x}-\mu}{s/\sqrt{n}}$$

The p-value for two-tailed, $df=n-1$ degrees of freedom, $t=\dfrac{\bar{x}-\mu}{s/\sqrt{n}}$ can be defined if $\bar{x}, \mu, s, n$ are given.

5)

Two-tailed test $p=2P(Z>1.63)=0.103101$