Who prepares your tax return? Refer to the Behavioral Research and Accounting (January 2015) study on income tax compliance, Exercise $5.50$ (p. 297). Recall that in a sample of 270 U.S. adult workers, the researchers found that $37 \%$ prepare their own tax return. Suppose an IRS tax consultant claims that $50 \%$ of all U.S. adult workers prepare their own tax return. Make an inference about this claim.

Use the applet Confidence Intervals for a Mean (the impact of not knowing the standard deviation) to compare proportions of $z$-intervals and $t$-intervals that contain the mean for a population with a skewed distribution. How does skewedness of the underlying distribution affect the proportions of $z$-intervals and $t$-intervals that contain the mean?

A random sample of 90 observations produced a mean

$$\overline { x } = 25.9$$

and a standard deviation s = 2.7. Find a 99% confidence interval for

$$\mu$$

Use the applet Confidence Intervals for a Mean (the impact of not knowing the standard deviation) to compare proportions of $z$-intervals and $t$-intervals that contain the mean for a population with a skewed distribution. Describe any patterns you observe between the proportion of $z$-intervals that contain the mean and the proportion of $t$-intervals that contain the mean as the sample size increases.

Use the applet Confidence Intervals for a Mean (the impact of not knowing the standard deviation) to compare proportions of $z$-intervals and $t$-intervals that contain the mean for a population with a skewed distribution. Repeat part a first for $n=10$ and then for $n=20$. Compare your results with those in part a.

A random sample of 90 observations produced a mean $\bar{x}=25.9$ and a standard deviation $s=2.7$.Find an approximate $90 \%$ confidence interval for $\mu$

A random sample of 90 observations produced a mean

$$\overline { x } = 25.9$$

and a standard deviation s = 2.7. Find a 95% confidence interval for the population mean

$$\mu$$

Use the applet Confidence Intervals for a Mean (the impact of not knowing the standard deviation) to compare proportions of $z$-intervals and $t$-intervals that contain the mean for a population with a skewed distribution. Using $n=5$ and the right skewed distribution with mean 50 and standard deviation 10 , run the applet several times. How do the proportions of $z$-intervals and $t$-intervals that contain the mean compare?

The Minneapolis Star Tribune (August 12, 2008) reported that 73% of Americans say that Starbucks coffee is overpriced. The source of this information was a national telephone survey of 1,000 American adults conducted by Rasmussen Reports. Find and interpret a 95% confidence interval for the parameter of interest.

The Minneapolis Star Tribune (August 12, 2008) reported that 73% of Americans say that Starbucks coffee is overpriced. The source of this information was a national telephone survey of 1,000 American adults conducted by Rasmussen Reports. Identify the parameter of interest in the study.

The Minneapolis Star Tribune (August 12, 2008) reported that 73% of Americans say that Starbucks coffee is overpriced. The source of this information was a national telephone survey of 1,000 American adults conducted by Rasmussen Reports. Identify the sample for the study.

The Minneapolis Star Tribune (August 12, 2008) reported that 73% of Americans say that Starbucks coffee is overpriced. The source of this information was a national telephone survey of 1,000 American adults conducted by Rasmussen Reports. Identify the population of interest in this study.

Do social robots walk or roll? Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study of the trend in the design of social robots, Exercise 5.44 (p. 296). The researchers obtained a random sample of 106 social robots through a Web search and determined that 63 were designed with legs, but no wheels.

Find a $99 \%$ confidence interval for the proportion of all social robots designed with legs, but no wheels. Interpret the result.

Do social robots walk or roll? Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study of the trend in the design of social robots, Exercise 5.44 (p. 296). The researchers obtained a random sample of 106 social robots through a Web search and determined that 63 were designed with legs, but no wheels.

Find a $99 \%$ confidence interval for the proportion of all social robots designed with legs, but no wheels. Interpret the result.