Practice with the Big Ideas Suppose it is claimed that 40% of adults support the practice of changing clocks twice a year in observance ofDaylight Saving Time. Believing this claimed value is too high, a sociologist surveys a random sample of 310 adults and nds that 113 of these adults say they support the practice of changing clocks twice a year in observance of Daylight Saving Time. 1. Remember that with hypothesis testing. we always begin with a set of two competing hypotheses. We have a hypothesis that puts forward the claim that is being tested about the population. We call this hypothesis the hypothesis. We then have a hypothesis that illustrates what we think is really going on in the population. We call this hypothesis the hypothesis. Using appropriate symbols= our hypotheses in this example are as follows: H0: {:3 0.40 H4: {:2 \""5 0.40 2. Look carefully at the hypotheses presented above. What does the symbol \6. 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 a sample outcome as extreme or more extreme than what we observed, if 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. (Hint: Don't forget that since a P-value is a probability, you will now need to take the percentile you get from Table B and divide it by 100 to convert it to a probability). 7. We determine if we have evidence against the null hypothesis, in favor of the alternative hypothesis, based on how the P-value compares to our chosen significance (or alpha) level. Remember that if the P-value is less than or equal to the significance level, we say that we have evidence against the null hypothesis. If the P-value is larger than the significance level, we do not have enough evidence against the null hypothesis (i.e., we cannot rule out the null hypothesis as a reasonable explanation for the observed sample outcome). If we assume here, with this example, that we are using a significance level of 0.05, what should we conclude? 8. Do you think your conclusion would have been different if the sample size had been larger? Please explain, and as you answer this, assume that a larger sample size would have resulted in the same sample proportion as what you computed to answer Question 4.Part 2: More Practice with the Big Ideas Now that you've had a chance to reason through a hypothesis testing problem from start to finish, let's attempt to solidify some of the big ideas with a new problem. A published report claims that 35% of college students have used an online dating site or app. Believing this claimed value is too low, a researcher surveys a random sample of n = 420 college students about their experiences with online dating sites and apps. A total of 166 of the surveyed students indicate that they have used online dating sites or apps. Use this information to conduct a hypothesis test at a significance (or alpha) level of 0.05. 9. What will the hypotheses be? Ho: Hai IMPORTANT: Before you go any further, double-check to make sure you are writing out your hypotheses using proper symbols and signs. 10. What is the sample proportion? Calculate this value below and round your answer to three decimal places. 11. Calculate the test statistic below, using the same formula that you used when answering Question 5. 12. Based on the test statistic you computed to answer Question 11, along with what you see in Table B, what should the P-value be?13. Based on the P-value you obtained and how it compares to the significance level of 0.05, what is your conclusion? 14. Look again at your answer to Question 13. If a smaller significance level had been chosen-like 0.01-would you have reached a different conclusion? Please explain. 15. Again, look back at how you answered Question 13. If a larger significance level had been chosen-like 0.10-would you have reached a different conclusion? Please explain. Stats in Action (Optional) In an earlier lab activity, we introduced you to an applet to help you compute a confidence interval. We can use that same applet, from the Art of Stat site, to conduct a hypothesis test. https://istats.shinyapps.io/Inference_prop/ Once you open the applet, go to where it says "Type of Inference" on the left side and select Significance Test. In the upper left corner, where it says "Enter Data," use the dropdown menu to select Number of Successes. There, you will type in a Sample Size and then the # of Successes. As an example, if you want to try to do this with the example from Part 1 of this activity, the sample size is 310 and the number of successes is 113. Once you type in these numbers, you'll see some output appear on the right side of screen. You'll then want to type in a "Null Value" (i.e., the value of p), and select the appropriate direction for the Alternative hypothesis (i.e., Two-sided, Less, or Greater). Notice the output gives you the sample proportion, the test statistic, and the P-value. Just keep in mind that the test statistic and P-value you get from using the applet might differ slightly from what you compute by hand and obtain from Table B