Paige M. answered • 05/31/20

College freshman tutor with experience in advanced mathematics

For this problem, you would need to conduct a **1-proportion z-test**. The key indicator that you would need to do a proportions test is that the problem states that your observed proportion is "25 out of 400," which is 0.0625. The procedure you would follow may differ from mine, but I like to use the acronym, "PHANTOMS" when I conduct hypothesis tests. Define your **parameters. **State your **hypotheses**. **Assess** the conditions. **Name** the test. Calculate the **test statistic**. **Obtain** a P-value. **Make **a decision. **State **your conclusion in context.

a.) Since proportion tests are used to generalize results to the entire population, your null hypothesis would be that **p = 0.05** ; not p-hat= 0.05. The problem says that the director company claims that more than 5% of all its subscribers would pay for the channel, so, correspondingly, your alternative hypothesis would be **p > 0.05**.

b.) The problem does not give a specific percentage for the confidence interval, so we cannot make any further calculations regarding the value of z*. However, this is the procedure to find the z-statistic. Since this is a 1-proportion z-test, we would use the formula p̂ - p0 / sqrt [p0(1-p0) / n], where p̂ is your hypothesized proportion **(0.05),** p0 is your observed proportion **(0.0625),** and n is your sample size (**400**). From there, just plug the numbers into the equation to find your z-statistic. Or, if you decide to run the test on your graphing calculator, enter **0.05** for hypothesized proportion, **25** for x, and **400** for n.

c.) After plugging the numbers into the equation or your graphing calculator, you should get a P-value of approximately **0.1257**.

d.) Now, we need to make a decision. In this case, since our P-value is greater than alpha (0.1257 > 0.05), we **fail to reject the null hypothesis.**

e.) Now, you need to write your conclusion in context. For this problem, you should write something like this: At 5% significance, we do **not** have enough evidence to conclude that the marketing director's claim that more than 5% of all the company's subscribers would pay an extra $10 a month to access the new sports channel.

Hope this helped! :)