Test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution.

In a Pew Research Center poll of 745 randomly selected adults, 589 said that it is morally wrong to not report all income on tax returns. Use a 0.01 significance level to test the claim that 75% of adults say that it is morally wrong to not report all income on tax returns.

The TI-83/84 Plus calculator can be used to generate random data from a normally distributed population. The command randNorm(74, 12.5, 100) generates 100 values from a normally distributed population with $\mu=74$ and $\sigma=12.5$ (for pulse rates of women). One such generated sample of 100 values has a mean of $74.4$. Assume that $\sigma$ is known to be $12.5$ and use a $0.05$ significance level to test the claim that the sample actually does come from a population with a mean equal to 74. Based on the results, does it appear that the calculator's random number generator is working correctly? The population standard deviation is unknown.

Find the $P$-value obtained when testing the claim that $p=0.75$ when given sample data resulting in a test statistic of $z=1.20$.

A hypothesis test is conducted with a $0.05$ significance level so that there is a 0.05 chance of making the mistake of rejecting a true null hypothesis. If two different independent hypothesis tests are conducted with a $0.05$ significance level, what is the possibility that both conclusions are mistakes of rejecting a true null hypothesis?

Find the test statistic and critical value(s). Also, use the mentioned table to find limits containing the P-value, then determine whether there is sufficient evidence to support the given alternative hypothesis.

Precipitation Amounts $H_1: \sigma \neq 0.25, \alpha=0.01, n=26, s=0.18$.

Test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise.

A simple random sample of 50 adults is obtained, and each person's red blood cell count (in cells per microliter) is measured. The sample mean is $5.23$. The population standard deviation for red blood cell counts is $0.54$. Use a $0.01$ significance level to test the claim that the sample is from a population with a mean less than $5.4$, which is a value often used for the upper limit of the range of normal values. What do the results suggest about the sample group?

Make a decision about the given claim. Use only the rare event rule stated in the mentioned section, and make subjective estimates to determine whether events are likely. For example, if the claim is that a coin favors heads and sample results consist of 11 beads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favors beads.

Claim: Movie patrons have IQ scores with a standard deviation that is less than the standard deviation of 15 for the general population. A simple random sample of 40 movie patrons results in IQ scores with a standard deviation of 14.8.

Refer to the histogram provided for the mentioned exercise and construct the frequency distribution that summarizes the outcomes. Then find the mean of the 100 outcomes.

Find the critical value(s) obtained when using a $0.05$ significance level for testing the claim that $\mu=100$ when given sample data consisting of $\bar{x}=90$, $s=10$, and $n=20$.

Test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise.

In the manual "How to Have a Number One the Easy Way," by KL.F Publications, it is stated that a song "must be no longer than three minutes and thirty seconds" (or 210 seconds). A simple random sample of 40 current hit songs results in a mean length of 252.5 sec. (The songs are by Timberlake, Furtado, Daughtry, Stefani, Fergie, Akon, Ludacris, etc.) Assume that the standard deviation of song lengths is 54.5 sec. Use a $0.05$ significance level to test the claim that the sample is from a population of songs with a mean greater than 210 sec. What do these results suggest about the advice given in the manual?

In a survey, 1640 out of 2246 randomly selected adults in the United States said that they use cell phones while driving (based on data from Zogby International). When testing the claim that the proportion of adults who use cell phones while driving is equal to 75% the TI- 83/84 Plus calculator display on the top of the next page is obtained. Use the results from the display with a $0.05$ significance level to test the stated claim.

Make a decision about the given claim. Use only the rare event rule stated in the mentioned section, and make subjective estimates to determine whether events are likely. For example, if the claim is that a coin favors heads and sample results consist of 11 beads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favors beads.

Claim: The mean pulse rate (in beats per minute) of students of the author is less than 75. A simple random sample of students has a mean pulse rate of 74.4.

The TI-83/84 Plus calculator can be used to generate random data from a normally distributed population. The command randNorm(74, 12.5, 100) generates 100 values from a normally distributed population with $\mu=74$ and $\sigma=12.5$ (for pulse rates of women). One such generated sample of 100 values has a mean of $74.4$ and a standard deviation of 11.7. Assume that $\sigma$ is known to be $12.5$ and use a $0.05$ significance level to test the claim that the sample actually does come from a population with a mean equal to 74. Based on the results, does it appear that the calculator's random number generator is working correctly?

Determine whether the hypothesis test involves a sampling distribution of means that is a normal distribution, Student t distribution, or neither:

Claim about daily rainfall amounts in Boston: $\mu<0.20$ in. Sample data: $n=19$, $\bar{x}=0.10 \mathrm{in}, s=0.26 \mathrm{in}$. The sample data appear to come from a population with a distribution that is very far from normal, and $\sigma$ is unknown.