Find the critical value z** _{α}**

_{/2}that corresponds to the given confidence level.

99%

z** _{α}**

_{/2 }=

**2.575**

Express the confidence interval 0.222 < 0.444 in the form p̂ ± E.

p̂ ± E =
**0.333** ± **0.111**

*p̂ = (upper +
lower confidence limit) ÷ 2*

*= (0.444 + 0.222) ÷ 2*

*= 0.333*

*E = (upper – lower confidence limit) ÷ 2*

*= (0.444 – 0.222) ÷ 2*

*= 0.111*

A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 320 babies were born, and 256 of them were girls.

Use the sample data to construct a 99% confidence interval estimate of the percentage of girls born.

Based on the result, does the method appear to be effective?

**0.742** < p < **0.858**

**Yes, the proportion of girls is significantly different from 0.5.**

A genetic experiment with peas resulted in one sample of offspring that consisted of 415 green peas and 159 yellow peas.

- Construct a 95% confidence interval to estimate of the percentage of yellow peas.
- It was expected that 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not 25%, do the results contradict expectations?

**0.240** < p < ** 0.314**

No, the confidence interval includes 0.25, so the true percentage could easily equal 25%

In a poll of 546 human resource professionals, 39.4% said that body piercings and tattoos were big grooming red flags.

- Among the 546 human resource professionals who were surveyed, how many of them said that body piercings and tattoos were big grooming red flags?
- Construct a 99% confidence interval estimate of the proportion of all human resource professionals believing that body piercings and tattoos are big grooming red flags.
- Repeat part (b) using a confidence level of 80%.
- Compare the confidence intervals from parts (b) and (c) and identify the interval that is wider. Why is it wider?

**a. 215**

*546 x 39.4% = 215.124*

**b. 0.340** < p
<** 0.448**

**c.** ** 0.367** < p
<** 0.421**

**d.** The
**99**% confidence interval is wider than the
**80**% confidence interval. As the confidence
interval widens, the probability that the confidence interval
actually does contain the population parameter increases.

During a period of 11 years 1074 of the people selected for grand jury duty were sampled, and 42% of them were immigrants.

Use the sample data to construct a 99% confidence interval estimate of the proportion of grand jury members who were immigrants.

Given that among the people eligible for jury duty, 54.7% of them were immigrants, does it appear that the jury selection process was somehow biased against immigrants?

** 0.381** < p
<** 0.459**

** Yes, the confidence
interval does not include the true percentage of immigrants.**

Use the given data to find the minimum sample size required to estimate a population proportion or percentage.

Margin of error: 0.03; confidence level 90%; p̂ and q^ unknown

n = **752**

Use the given data to find the minimum sample size required to estimate a population proportion or percentage.

Margin of error: four percentage points; confidence level 95%; from a prior study, p̂ is estimated by the decimal equivalent of 54%

n = **597**

A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.04 with 99% confidence if

**a)** she uses a previous estimate of 0.52?

**b)** she does not use any prior estimates?

**a)** n = **1035**

**b)** n = **1037**

The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first determine the percentage of adults who have heard of the brand. How many adults must he survey in order to be 80% confident that his estimate is within six percentage points of the true population percentage?

- Assume that nothing is known about the percentage of adults who have heard of the brand.

**a)** n = **114**

**b)** n = **49**

**c)** No, a sample of students at the nearest college is
a convenience sample, not a simple random sample, so it is very
possible that the results would not be representative of the
population of adults.

*Just surveying the adults at the nearest college is a convenience
sample, which is not necessarily representative of the population.*

Which concept below is NOT a main idea of estimating a population proportion?

- We can use a sample proportion to construct a confidence interval to estimate the true value of a population proportion.
- Using a sample statistic to estimate the population proportion is utilizing descriptive statistics.
- Knowing the sample size necessary to estimate a population proportion is important.
- The sample proportion is the best point estimate of the population proportion.

**Using a sample statistic to estimate the population proportion
is utilizing descriptive statistics.**

*Using a sample statistic to estimate the population proportion is
not utilizing descriptive statistics; it is utilizing inferential statistics.*

Which of the following is NOT an observation about critical values?

- The number z
_{ α/2}is a critical value that corresponds to an area of 1 –**α**/2 to its left. - The number
z
_{ α/2}is a critical value that is a z score with the property that it separates an area of**α**/2 in the right tail of the standard normal distribution. - A critical value is the number on the borderline separating sample statistics that are likely to occur from those that are unlikely to occur.
- A critical value is the area in the right-tail region of the standard normal curve.

**A critical value is the area in the right-tail region of the
standard normal curve.**

*A critical value is a z-score associated with the area in the
right-tail region of the standard normal curve, not the area itself.*

When analyzing polls, which of the following is NOT a consideration?

- The quality of the poll results usually depends on the sampling method and the size of the sample, but not the size of the population.
- The sample should be a voluntary response or convenience sample.
- The sample size should be provided.
- The confidence level should be provided.

**The sample should be a voluntary response or convenience sample.**

*The sample should be a simple random sample as voluntary response
or convenience samples introduce bias and reduce the reliability of
any poll results.*