General Statistics: Ch 7 Quiz

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This course is designed to acquaint the student with the principles of descriptive and inferential statistics. Topics will include: types of data, frequency distributions and histograms, measures of central tendency, measures of variation, probability, probability distributions including binomial, normal probability and student's t distributions, standard scores, confidence intervals, hypothesis testing, correlation, and linear regression analysis. This course is open to any student interested in general statistics and it will include applications pertaining to students majoring in athletic training, pre-nursing and business.
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1

Find the critical value z α /2 that corresponds to the given confidence level.

99%

z α /2 = 2.575

2

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

3

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.

4

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

  1. Construct a 95​% confidence interval to estimate of the percentage of yellow peas.
  2. 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%

5

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

  1. Among the 546 human resource professionals who were​ surveyed, how many of them said that body piercings and tattoos were big grooming red​ flags?
  2. 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.
  3. Repeat part​ (b) using a confidence level of​ 80%.
  4. 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.

6

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.

7

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

8

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

9

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

10

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?

  1. 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.

11

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

  1. We can use a sample proportion to construct a confidence interval to estimate the true value of a population proportion.
  2. Using a sample statistic to estimate the population proportion is utilizing descriptive statistics.
  3. Knowing the sample size necessary to estimate a population proportion is important.
  4. 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.

12

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

  1. The number z α/2 is a critical value that corresponds to an area of 1 – α/2 to its left.
  2. 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.
  3. A critical value is the number on the borderline separating sample statistics that are likely to occur from those that are unlikely to occur.
  4. 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.

13

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

  1. 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.
  2. The sample should be a voluntary response or convenience sample.
  3. The sample size should be provided.
  4. 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.