At certain points during the COVID-19 pandemic, many of us had no choice but to complete our work from home. For some employees, working from home was so rewarding that they found themselves wishing they could work from home indefinitely. One report, in fact, claimed that 75% of workers with jobs that could be done from home said that if they had a choice, they'd like to continue working from home all or most of the time, even when it's safe for them to work outside of their home. Believing this claimed value is too high, a researcher surveys a random sample of 945 adult employees and finds that 693 of them would like to continue working from home all or most of the time after COVID-19 restrictions ease. 1. If we want to use the above information to conduct a hypothesis test, we need to begin with two competing hypotheses. The first hypothesis is the initial claim to be tested about the population. We would write this claim as H.: p=0.75. What do we call this hypothesis? 2. The second hypothesis we begin with illustrates our theory, or what we believe is actually going on in the population (i.e., the reason we are conducting the hypothesis test in the first place). Here, we would write this second hypothesis as H.: p<0.75. What do we call this hypothesis? 3. Look carefully at the hypotheses above, within Questions I and 2. Notice that both hypotheses include the symbol "p." What does "p" stand for? 4. Look again at the hypothesis presented within Question 2. Notice that there is a "<" (or less than) sign within that hypothesis. Why exactly would we be using the "<"sign as opposed to the ">" (or greater than) sign? Dashboard Calendar To Do n Notifications Inbox 5. Before we can conduct our hypothesis test, we need to determine the sample proportion. Recall that 945 employees were surveyed, and 693 of them said they would like to continue working from home all or most of the time. What will the sample proportion (or) be? Please compute this value below and round your answer to three decimal places. 6 To be able to conduct a hypothesis test, we will now need to compute a test statistic (using the following formula). Please attempt to compute this test statistic below, showing as much work as you can. P(1-P) Hint: As you engage in calculations, we recommend you first determine the value in the denominator and then divide the numerator by that value. Round the value in the denominator to about three decimal places, at least, so you can be as precise as possible. The test statistic itself, once computed, should be rounded to exactly one decimal place. 7. As part of the process of conducting a hypothesis test, we need to find what's called a probability value, or a P-value for short. This P-value value tells us something about how likely it would be to observe results as extreme or more extreme than what we observed, if we assume the null hypothesis is really true. Based on the test statistic you calculated to answer Question 6, what should the P-value be equal to? Please use Table B to find this P-value, and don't forget that since a P-value is a probability, you need to now take the percentile you get from Table B and divide it by 100 to convert it to a probability. Hint: As you engage in calculations, we recommend you first determine the value in the denominator and then divide the numerator by that value. Round the value in the denominator to about three decimal places, at least, so you can be as precise as possible. The test statistic itself, once computed, should be rounded to exactly one decimal place. 7. As part of the process of conducting a hypothesis test, we need to find what's called a probability value, or a P-value for short. This P-value value tells us something about how likely it would be to observe results as extreme or more extreme than what we observed, if we assume the null hypothesis is really true. Based on the test statistic you calculated to answer Question 6, what should the P-value be equal to? Please use Table B to find this P-value, and don't forget that since a P-value is a probability, you need to now take the percentile you get from Table B and divide it by 100 to convert it to a probability. & Remember the competing hypotheses we started off with at the beginning of our significance test. H₂: p=0.75 H,: p<0.75 Do we have support in favor of or against the null hypothesis? To figure this out, we now need to see how our P-value compares to our chosen significance (or alpha) level. If we assume here that we are using a significance level (or an alpha level) of 0.05, what should we conclude? Please explain the reason for your answer.