Question

in a sample of 173 employees, you find that 8% of them take public transport to work. test the claim using a 1% level of significance.
a. what type of test will be used in this problem? select an answer
b. enter the null hypothesis for this test. $h_0$:? ?
c. enter the alternative hypothesis for this test. $h_1$:? ?
d. is the original claim located in the null or alternative hypothesis? select an answer
e. what is the test statistic for the given statistics?
f. what is the p - value for this test?
g. what is the decision based on the given statistics? select an answer
h. what is the correct interpretation of this decision?

Explanation:

Step1: Identify test type

Since we are testing a claim about a proportion ($8\%$ of employees take public transport), a one - proportion z - test will be used.

Step2: Formulate null hypothesis

The null hypothesis $H_0$ for a test about a proportion $p$ is usually a statement of no effect or no difference. If the claim is about a proportion $p$, and we assume the claim is the status - quo, $H_0:p = 0.08$.

Step3: Formulate alternative hypothesis

The alternative hypothesis $H_1$ depends on the nature of the test. If we are just testing if the proportion is different from the claimed value, $H_1:p
eq0.08$.

Step4: Locate original claim

The original claim could be either in the null or alternative hypothesis. If the claim is that the proportion is $8\%$, the claim is in the null hypothesis.

Step5: Calculate test - statistic

The formula for the one - proportion z - test statistic is $z=\frac{\hat{p}-p}{\sqrt{\frac{p(1 - p)}{n}}}$, where $\hat{p}$ is the sample proportion, $p$ is the hypothesized proportion under the null hypothesis, and $n$ is the sample size. But since the sample size and sample proportion are not given in the problem statement, we cannot calculate the exact value.

Step6: Find p - value

The p - value for a two - tailed one - proportion z - test is $2P(Z > |z|)$ if $z$ is the calculated test statistic. Without the test statistic, we cannot calculate the p - value.

Step7: Make a decision

We compare the p - value with the significance level $\alpha = 0.01$. If $p - value<\alpha$, we reject the null hypothesis; if $p - value\geq\alpha$, we fail to reject the null hypothesis.

Step8: Interpret the decision

If we reject the null hypothesis, we conclude that there is sufficient evidence to support the claim that the proportion of employees who take public transport is different from $8\%$ at the $1\%$ significance level. If we fail to reject the null hypothesis, we conclude that there is not sufficient evidence to support the claim that the proportion is different from $8\%$ at the $1\%$ significance level.

Answer:

a. One - proportion z - test
b. $H_0:p = 0.08$
c. $H_1:p
eq0.08$
d. Null hypothesis
e. Cannot be calculated without sample size and sample proportion
f. Cannot be calculated without test statistic
g. Cannot be determined without p - value
h. If reject $H_0$: There is sufficient evidence that the proportion of employees taking public transport is different from $8\%$ at $1\%$ significance level. If fail to reject $H_0$: There is not sufficient evidence that the proportion of employees taking public transport is different from $8\%$ at $1\%$ significance level.