BTATS Bonus Quiz

The contingency table below provides frequencies for the preferred type of exercise for people under the age of 35 and those 35 years of age or older. Find the probability that an individual prefers biking.

0.2868

An auto parts chain asked customers to complete a survey rating the chain's customer service as average, above average, or below average. The following shows the results from the survey: The proportion of customers who felt the customer service was Average is the closest to _______.

0.33

Consider the following cumulative distribution function for the discrete random variable X. X: 1 2 3 4 P(X ≤ x) 0.3 0.44 0.72 1.00 What is the probability that X is greater than 2?

0.56

A confidence interval was used to estimate the proportion of statistics students that are female. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Using the information above, what total size sample would be necessary if we wanted to estimate the true proportion to within ±0.08 using 95% confidence?

150

A bowler's scores for a sample of six games were 172 168 188 190 172 182 174 The bowler's modal score is _____.

172

Statisticians like precision in their interval estimates. A low margin of error is needed to achieve this. Which of the following supports this when selecting sample sizes?

A larger sample size reduces the margin of error.

A 99% confidence interval for the population mean yields the following results: [−3.79, 5.86]. At the 1% significance level, what decision should be made regarding the following hypothesis test with Ho:μ = 0,HA:μ ≠ 0?

Do not reject Ho; we cannot conclude that the mean differs from zero.

True or False? A pie chart is a segmented circle that portrays the categories and relative sizes of some quantitative variable.

False

True or False? Like the z distribution, the t-df distribution is symmetric around 0, bell-shaped, and with tails that approach the horizontal axis and eventually cross it.

False

True or False? Scatterplot is a graphical tool that is focused on describing one variable.

False

Professors at a local university earn an average salary of $80,000 with a standard deviation of $6,000. The salary distribution is approximately bell-shaped. What can be said about the percentage of salaries that are less than $68,000 or more than $92,000?

It is about 5%.

Let P(A) = 0.6, P(B) = 0.5, and P(A ⋃ B^c)= 0.1. Calculate P(A|B)

P(A ⋃ B)= 1 - P((A ⋃ B)^c) P(A ⋂ B)= P(A) + P(B) - P(A ⋃ B) P(A|B)= P(A ⋂ B)/ P(B) 0.40

A basketball coach wants to know how many free throws an NBA player shoots during the course of an average practice. The coach takes a random sample of 43 players and finds the average number of free throws shot per practice was 225 with a standard deviation of 35. Construct a 99% confidence interval for the average number of free throws in practice.

[210.5992, 239.4008]

It is possible to directly compare the results of a confidence interval estimate to the results obtained by testing a null hypothesis if

a two-tail test for μ is used.

If event A and event B cannot occur at the same time, then events A and B are said to be

mutually exclusive

Find the minimum sample size when we want to construct a 95% confidence interval on the population proportion for the support of candidate A in the following mayoral election. Candidate A is facing two opposing candidates. In a pre-selected poll of 100 residents, 22 supported candidate B and 14 supported candidate C. The desired margin of error is 0.06.

n = 246

In the construction of confidence intervals, if all other quantities are unchanged, an increase in the sample size will lead to a ______ interval.

narrower

A ________ is a numerical quantity not computed from the data of a sample and is the size of the critical region used in reaching a decision on whether or not to reject the null hypothesis.

significance level

A company decided to test the hypothesis that the average time a company's employees are spending to check their private e-mails at work is more than 6 minutes. A random sample of 40 employees were selected and they averaged 6.6 minutes. It is believed that the population standard deviation is 1.7 minutes. The α is set to 0.05. The p-value for this hypothesis test would be ______.

0.0128

Suppose that, on average, electricians earn approximately µ = $54,000 per year in the United States. Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = $12,000. What is the probability that the average salary of four randomly selected electricians exceeds $60,000?

0.1587

Peter applied to an accounting firm and a consulting firm. He knows that 30% of similarly qualified applicants receive job offers from the accounting firm, while only 20% of similarly qualified applicants receive job offers from the consulting firm. Assume that receiving an offer from one firm is independent of receiving an offer from the other. What is the probability that both firms offer Peter a job?

P(accounting) = 0.30 P(consulting) = 0.20 Assuming that receiving an offer from one firm is independent of receiving an offer from the other P(accounting and consulting) = P(accounting)*P(consulting)= 0.30*0.20= 0.06

The accompanying (bar) chart shows the number of books written by each author in a collection of cookbooks. What type of data is being represented?

Qualitative, nominal

Consider the following probability distribution: xi= 0, 1, 2, 3 P(X=xi)= 0.1, 0.2, 0.4, 0.3 The expected value is?

Sum of P(X=xi) 0.1+0.2+0.4+0.3= 1.9

Scores on a business statistics final exam are normally distributed with a mean of 74 and standard deviation of 8. z value for the exam score of 84 equals ______.

To convert x value to z value we should use the following equation: = (84 − 74)/8 = 1.25

True of False? A confidence interval provides a value that, with a certain measure of confidence, is the population parameter of interest.

false, A confidence interval provides a range of values that, with a certain level of confidence, contains the population parameter of interest.

A 99% confidence interval estimate can be interpreted to mean that

if all possible samples are taken and confidence interval estimates are developed, 99% of them would include the true population mean somewhere within their interval we have 99% confidence that we have selected a sample whose interval does include the population mean

A ________ is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis.

test statistic

In stratified random sampling, the population is first divided up into mutually exclusive and collectively exhaustive groups, called strata. A stratified sample includes randomly selected observations from each stratum, which are proportional to the stratum's size.

true

When a statistic is used to estimate a parameter, the statistic is referred to as an estimator. A particular value of the estimator is called an estimate.

true

If, as a result of a hypothesis test, we do not reject the null hypothesis when it is false, then we have committed

type II error