Statistics Questions & Answers

Construct the confidence interval for the population mean \( \mu \). \( \mathrm{c}=0.98, \overline{\mathrm{x}}=4.4, \sigma=0.3 \), and \( \mathrm{n}=52 \) A \( 98 \% \) confidence interval for \( \mu \) is ( \( \square . \square \). (Round to two decimal places as needed.)

In a random sample of 20 people, the mean commute time to work was 34.8 minutes and the standard deviation was 7.2 minutes. Assume the population is normally distributed and use a t-distribution to construct a \( 98 \% \) confidence interval for the population mean \( \mu \). What is the margin of error of \( \mu \) ? Interpret the results. The confidence interval for the population mean \( \mu \) is ( (Round to one decimal place as needed.) The margin of error of \( \mu \) is (Round to one decimal place as needed.) Interpret the results. B. With \( 98 \% \) confidence, it can be said that the population mean commute time is between the bounds of the confidence interval. C. With \( 98 \% \) confidence, it can be said that the commute time is between the bounds of the confidence interval. D. If a large sample of people are taken approximately \( 98 \% \) of them will have commute times between the bounds of the confidence interval.

Use the confidence interval to find the estimated margin of error. Then find the sample mean. A biologist reports a confidence interval of \( (2.3,3.3) \) when estimating the mean height (in centimeters) of a sample of seedlings. The estimated margin of error is The sample mean is

Use the confidence interval to find the margin of error and the sample mean. \( (0.604,0.740) \) The margin of error is \( \square \). The sample mean is \( \square \).

Let p be the population proportion for the following condition. Find the point estimates for \( p \) and \( q \). In a survey of 1135 adults from country \( \mathrm{A}, 514 \) said that they were not confident that the food they eat in country A is safe. The point estimate for \( p, \hat{p} \), is (Round to three decimal places as needed.) The point estimate for \( q, \hat{q} \), is (Round to three decimal places as needed.)

Use the given confidence interval to find the margin of error and the sample mean. The sample mean is \( \square \). (Type an integer or a decimal.) The margin of error is \( \square \). (Type an integer or a decimal.)

A researcher wishes to estimate, with 95\% confidence, the population proportion of likely U.S. voters who think Congress is doing a good or excellent job. Her estima must be accurate within \( 3 \% \) of the true proportion. (a) No preliminary estimate is available. Find the minimum sample size needed. (b) Find the minimum sample size needed, using a prior study that found that \( 42 \% \) of the respondents said they think Congress is doing a good or excellent job. (c) Compare the results from parts (a) and (b). (a) What is the minimum sample size needed assuming that no prior information is available? \( \mathrm{n}=\square \) (Round up to the nearest whole number as needed.) (b) What is the minimum sample size needed using a prior study that found that \( 42 \% \) of the respondents said they think Congress is doing a good or excellent job? \( n=\square \) (Round up to the nearest whole number as needed.) (c) How do the results from (a) and (b) compare? A. Having an estimate of the population proportion reduces the minimum sample size needed. B. Having an estimate of the population proportion has no effect on the minimum sample size needed. C. Having an estimate of the population proportion raises the minimum sample size needed.

16 Use technology to construct the confidence intervals for the population variance \( \sigma^{2} \) and the population standard deviation \( \sigma \). Assume the sample is taken from a normally distributed population. \[ =0.99, s=34, n=20 \] The confidence interval for the population variance is ( \( \square \). (Round to two decimal places as needed.) The confidence interval for the population standard deviation is ( (Round to two decimal places as needed.)

THREE (3) dispersion measurements

6 The positive square root of the average of squares of deviations of the values from mean is called the \( \begin{array}{ll}\text { (a) range. } & \text { (b) arithmetic mean. } \\ \text { (c) standard deviation. } & \text { (d) mode. }\end{array} \)