Answer to Question #105331 in Statistics and Probability for Katenda

Question

Question 9

Which of the following is not a step in hypothesis testing?
(1) Formulate the null and alternative hypothesis.
(2) Specify the level of significance.
(3) Determine the test statistic, critical value and p-value.
(4) Determine the rejection region.
(5) None of the above.

Question 11

What is the value of the test statistic?
(1) -3.33
(2) 2.58
(3) 1.96
(4) 1.645
(5) 0.0012

Question 12

What is the critical value?
(1) -3.33
(2) 2.58
(3) 1.96
(4) 1.645
(5) 0.0012

Question 13

What is the p-value?
(1) 0.05
(2) 0.01
(3) 0.0024
(4) p–value < 0.002
(5) None of the above

Answer 1

Question 9 

Which of the following is not a step in hypothesis testing?

(1) Formulate the null and alternative hypothesis.

(2) Specify the level of significance.

(3) Determine the test statistic, critical value and p-value.

(4) Determine the rejection region.

(5) None of the above.

Solution

(5) None of the above.

Botlhale, a practicing Statistician is tasked with investigating whether the population mean of a random variable $X$ is different from $100.$ She has the following additional information to help her with the investigation: $\alpha=0.01, \sigma=3, \bar {X}=99,$ and $n=100.$

Question 11

What is the value of the test statistic?

(1) -3.33

(2) 2.58

(3) 1.96

(4) 1.645

(5) 0.0012 

Solution

$$Z={\bar{X}-\mu \over \sigma/\sqrt{n}}={99-100\over 3 \sqrt{100}}\approx-3.33$$

(1) -3.33

Question 12

What is the critical value?

(1) -3.33

(2) 2.58

(3) 1.96

(4) 1.645

(5) 0.0012 

Solution

The z-critical values for a two-tailed test, for a significance level of $\alpha=0.01:z_c=-2.58$ and $z_c=2.58$

(2) 2.58

Question 13

What is the p-value?

(1) 0.05

(2) 0.01

(3) 0.0024

(4) p–value < 0.002

(5) None of the above

Solution

$p-$Value from Z Score Calculator: $Z=-3.33, \alpha=0.01,$ two-tailed

The $p$ -value is $0.000868$

(4) p–value < 0.002