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The area in the right tail more extreme than \(z=3.0\)

Exercises 5.7 to 5.12 include a set of hypotheses, some information from one or more samples, and a standard error from a randomization distribution. Find the value of the standardized \(z\) -test statistic in each situation. Test \(H_{0}: \mu_{1}=\mu_{2}\) vs \(H_{a}: \mu_{1}>\mu_{2}\) when the samples have \(n_{1}=n_{2}=50, \bar{x}_{1}=35,4, \bar{x}_{2}=33.1, s_{1}=\) 1.28 , and \(s_{2}=1.17\). The standard error of \(\bar{x}_{1}-\bar{x}_{2}\) from the randomization distribution is \(0.25 .\)

In Exercises 5.13 and \(5.14,\) find the p-value based on a standard normal distribution for each of the following standardized test statistics. (a) \(z=0.84\) for a right-tail test for a difference in two proportions (b) \(z=-2.38\) for a left-tail test for a difference in two means (c) \(z=2.25\) for a two-tailed test for a proportion

In Exercises 5.13 and \(5.14,\) find the p-value based on a standard normal distribution for each of the following standardized test statistics. (a) \(z=-1.08\) for a left-tail test for a mean (b) \(z=4.12\) for a right-tail test for a proportion (c) \(z=-1.58\) for a two-tailed test for a difference in means

Effect of Organic Potatoes after 11 Days After 11 days, the proportion of fruit flies eating organic potatoes still alive is 0.68 , while the proportion still alive eating conventional potatoes is \(0.66 .\) The standard error for the difference in proportions is \(0.030 .\)

How Do You Get Your News? A study by the Pew Research Center \(^{9}\) reports that in \(2010,\) for the first time, more adults aged 18 to 29 got their news from the Internet than from television. In a random sample of 1500 adults of all ages in the US, \(66 \%\) said television was one of their main sources of news. Does this provide evidence that more than \(65 \%\) of all adults in the US used television as one of their main sources for news in \(2010 ?\) A randomization distribution for this test shows \(S E=0.013\). Find a standardized test statistic and compare to the standard normal to find the p-value. Show all details of the test.

To Study Effectively, Test Yourself! Cognitive science consistently shows that one of the most effective studying tools is to self-test. A recent study \(^{10}\) reinforced this finding. In the study, 118 college students studied 48 pairs of Swahili and English words. All students had an initial study time and then three blocks of practice time. During the practice time, half the students studied the words by reading them side by side, while the other half gave themselves quizees in which they were shown one word and had to recall its partner. Students were randomly assigned to the two groups, and total practice time was the same for both groups, On the final test one week later, the proportion of items correctly recalled was \(15 \%\) for the reading-study group and \(42 \%\) for the self-quiz group. The standard error for the difference in proportions is about 0.07 . Test whether giving self-quizzes is more effective and show all details of the test. The sample size is large enough to use the normal distribution.

Penalty Shots in World Cup Soccer A study \(^{11}\) of 138 penalty shots in World Cup Finals games between 1982 and 1994 found that the goalkeeper correctly guessed the direction of the kick only \(41 \%\) of the time. The article notes that this is "slightly worse than random chance." We use these data as a sample of all World Cup penalty shots ever. Test at a \(5 \%\) significance level to see whether there is evidence that the percent guessed correctly is less than \(50 \%\). The sample size is large enough to use the normal distribution. The standard error from a randomization distribution under the null hypothesis is \(S E=0.043 .\)

Dogs Ignore an Unreliable Person A study12 investigated whether dogs change their behavior depending on whether a person displays reliable or unreliable behavior. Dogs were shown two containers, one empty and one containing a dog biscuit. An experimenter pointed to one of the two containers. If the experimenter pointed to the container with the treat on the first trial, 16 of 26 dogs followed the experimenter's cue on the second trial. However, if the experimenter misled the dog on the first trial, only 7 of 26 dogs followed the cue on the second trial. Test to see if the proportion following the cue is different depending on whether the person exhibited reliable or unreliable behavior. The standard error for the difference in proportions is \(0.138 .\) Use a \(5 \%\) significance level and show all details of the test.

Exercise and Gender The dataset ExerciseHours contains information on the amount of exercise (hours per week) for a sample of statistics students. The mean amount of exercise was 9.4 hours for the 30 female students in the sample and 12.4 hours for the 20 male students, A randomization distribution of differences in means based on these data, under a null hypothesis of no difference in mean exercise time between females and males, is centered near zero and reasonably normally distributed. The standard error for the difference in means, as estimated from the randomization distribution, is \(S E=2.38\). Use this information to test, at a \(5 \%\) level, whether the data show that the mean exercise time for female statistics students is less than the mean exercise time of male statistics students.