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There were 2430 Major League Baseball (MLB) games played in 2009 , and the home team won the game in \(54.9 \%\) of the games. \({ }^{23}\) If we consider the games played in 2009 as a sample of all MLB games, test to see if there is evidence, at the \(1 \%\) level, that the home team wins more than half the games. Show all details of the test.

Find endpoints of a t-distribution with 0.025 beyond them in each tail if the sample has size \(n=25 .\)

Find endpoints of a t-distribution with 0.005 beyond them in each tail if the sample has size \(n=40 .\)

Find the area in a t-distribution above 2.3 if the sample has size \(n=6\).

Use StatKey or other technology to generate a bootstrap distribution of sample means and find the standard error for that distribution. Compare the result to the standard error given by the Central Limit Theorem, using the sample standard deviation as an estimate of the population standard deviation. Mean price of used Mustang cars online (in \(\$ 1000\) s) using the data in MustangPrice with \(n=25,\) \(\bar{x}=15.98,\) and \(s=11.11\)

IQ tests scale the scores so that the mean IQ score is \(\mu=100\) and standard deviation is \(\sigma=15\). Suppose that 30 fourth graders in one class are given such an IQ test that is appropriate for their grade level. If the students are really a random sample of all fourth graders, what is the chance that the average IQ score for the class is above \(105 ?\)

A \(90 \%\) confidence interval for \(\mu\) using the sample results \(\bar{x}=3.1, s=0.4,\) and \(n=100\)

In Exercises 6.111 to \(6.114,\) what sample size is needed to give the desired margin of error in estimating a population mean with the indicated level of confidence? A margin of error within ±5 with \(95 \%\) confidence, assuming a previous sample had \(s=18\)

In Exercises 6.123 and \(6.124,\) find a \(95 \%\) confidence interval for the mean two ways: using StatKey or other technology and percentiles from a bootstrap distribution and using the t-distribution and the formula for standard error. Compare the results. Mean distance of a commute for a worker in Atlanta, using data in CommuteAtlanta with \(\bar{x}=18.156\) miles, \(s=13.798,\) and \(n=500\)

Find a \(95 \%\) confidence interval for the mean two ways: using StatKey or other technology and percentiles from a bootstrap distribution and using the t-distribution and the formula for standard error. Compare the results. Mean price of a used Mustang car online, in \$1000s, using data in MustangPrice with \(\bar{x}=15.98\), \(s=11.11,\) and \(n=25\)