Television networks rely heavily on ratings of TV shows when deciding whether to renew a show for another season. Suppose a network has decided that "Miniature Golf with the Stars" will only be renewed if it can be established that more than 12% of U.S. adults watch the show. A polling company asks a random sample of 2000 U.S. adults if they watch "Miniature Golf with the Stars." The network uses the data to perform a test of: H0: p = 0.12 HA: p > 0.12 where p is the true proportion of all U.S. adults who watch the show. Describe a Type I error and a Type II error in this setting. You find convincing evidence that the proportion of all U.S. adults who watch the show exceeds 0.12, when in reality it equals 0.12. You do not find convincing evidence that the proportion of all U.S. adults who watch the show exceeds 0.12 when in reality it is greater than 0.12.
Added by Shannon R.
Step 1
In this setting, a Type I error would occur if the network decides to renew "Miniature Golf with the Stars" based on the sample data, even though the true proportion of U.S. adults who watch the show is not actually greater than 12%. In other words, the network Show more…
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Television networks rely heavily on ratings of television shows when deciding whether to renew a show for another season. Suppose the Hyena network has decided that "Miniature Golf with the Stars" will only be renewed if it can be established that more than 12% of people in a nationwide poll watch the show. Let p be the true proportion of people in the country who watch the show. A random sample of 2500 US adults was taken and 275 said they watched the show. Construct a 90% interval for the true proportion of US adults who watch the show. a. Which interval should you use and what are the conditions? b. Calculate the interval. c. Interpret the interval.
T. L.
a. In a recent Super Bowl, a TV network predicted that 48% of the audience would express an interest in seeing one of its forthcoming television shows. The network ran commercials for these shows during the Super Bowl. The day after the Super Bowl, an Advertising Group sampled 58 people who saw the commercials and found that 31 of them said they would watch one of the television shows. Suppose you have the following null and alternative hypotheses for a test you are running: H0: p = 0.48 Ha: p < 0.48 Calculate the test statistic, rounded to 3 decimal places. z = b. In a recent Super Bowl, a TV network predicted that 58% of the audience would express an interest in seeing one of its forthcoming television shows. The network ran commercials for these shows during the Super Bowl. The day after the Super Bowl, an Advertising Group sampled 58 people who saw the commercials and found that 33 of them said they would watch one of the television shows. Suppose you have the following null and alternative hypotheses for a test you are running: H0: p = 0.58 Ha: p ≠ 0.58 Calculate the test statistic, rounded to 3 decimal places. z =
Danielle F.
(b) Suppose that the sample size had been 100 rather than 600 and that 45% of those in the sample indicated that they usually use social media while watching TV. Based on this sample of 100, is there convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV? Use a significance level of 0.05. State the appropriate null and alternative hypotheses. H0: p ≠ 0.5 versus Ha: p = 0.5 H0: p = 0.5 versus Ha: p ≠ 0.5 H0: p = 0.5 versus Ha: p < 0.5 H0: p = 0.5 versus Ha: p > 0.5 H0: p < 0.5 versus Ha: p > 0.5 Find the test statistic and P-value. (Use a table or technology. Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. Fail to reject H0. We do not have convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV. Reject H0. We do not have convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV. Reject H0. We have convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV. Fail to reject H0. We have convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV. (c) Explain why different conclusions were reached in the hypothesis tests of parts (a) and (b). Getting out of 600 people responding this way as opposed to out of 100 provides much ---Select--- evidence that fewer than half of Americans ages 14 to 18 years usually use social media while watching TV.
Qudsiya A.
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