Stats Test 2

Determine the point estimate of the population​ proportion, the margin of error for the following confidence​ interval, and the number of individuals in the sample with the specified​ characteristic, x, for the sample size provided. Lower bound=0.083​, upper bound=0.527​, n=1200

PE: Lower bound + upper bound/2 M of E: upper bond - lower bond/2 number of indiv.: PE(n)

A​ ________ ________ is the value of a statistic that estimates the value of a parameter.

Point Estimate

The procedure for constructing a confidence interval about a mean is​ _______, which means minor departures from normality do not affect the accuracy of the interval.

Robust

The​ _____ _____, denoted p​, is given by the formula p=​_____, where x is the number of individuals with a specified characteristic in a sample of n individuals.

Sample, Proportion, x/n

The approximate​ Z-score that corresponds to a right tail area of 0.45 is (Round to two decimals)

https://www.calculators.org/math/z-critical-value.php

Find the​ z-scores that separate the middle 21​% of the distribution from the area in the tails of the standard normal distribution.

https://www.easycalculation.com/statistics/percentile-to-z-score.php Use middle tail. Enter first negative number, then positive number. Ex: -0.27, 0.27

Determine the area under the standard normal curve that lies to the left of

https://www.zscorecalculator.com/

A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 35 adult Americans and asks them whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond​ yes, is approximately​ normal, how many more adult Americans does the researcher need to sample in the following​ cases? ​(a) 20​% of all adult Americans support the changes ​(b) 25​% of all adult Americans support the changes

n= 10/p(1-p) n-sample

The following data represent the level of health and the level of education for a random sample of 1464 residents. Complete parts​ (a) and​ (b) below.

​: Level of education and health are independent. H1​: Level of education and health are dependent. Statcrunch: Tables>Contingency> With summary>select categories Sum horizontally, divide each number by total

Suppose a simple random sample of size n=64 is obtained from a population with μ=88 and σ=32. ​(a) Describe the sampling distribution of x. ​(b) What is P x>94.2​? ​(c) What is P x≤79​? ​(d) What is P 84.4<x<96.6​?

(a) The distribution is approximately normal. (b) ux=88 ox = Z Stats> One Sample>With summary For P: Statcrunch: Calculator>Normal Use the ox for o!

If we reject the null hypothesis when the statement in the null hypothesis is​ true, we have made a Type​ _______ error.

1

The area under the normal curve to the right of μ equals

1/2

If we do not reject the null hypothesis when the statement in the alternative hypothesis is​ true, we have made a Type​ _______ error.

2

The​ _______ _______ is a statement of no change, no effect, or no difference.

Null Hypothesis

If the consequences of making a Type I error are​ severe, would you choose the level of​ significance, α​, to equal​ 0.01, 0.05, or​ 0.10?

0.01

In 1946​, an organization surveyed 1100 adults and​ asked, "Are you a total abstainer​ from, or do you on occasion​ consume, alcoholic​ beverages?" Of the 1100 adults​ surveyed, 352 indicated that they were total abstainers. In a recent​ survey, the same question was asked of 1100 adults and 275 indicated that they were total abstainers. Complete parts​ (a) and​ (b) below.

352/1100 275/1100 The sample size is less than​ 5% of the population size for each sample. The samples are independent. n1p1(1-pa)>=10... = =/ Proportion states>two samples If the population proportions are equal, one would expect a sample difference proportion greater than the absolute value of greater than the absolute value of the one observed in about 0 out of 100 repetitions of this experiment.

A researcher wants to show the mean from population 1 is less than the mean from population 2 in​ matched-pairs data. If the observations from sample 1 are Xi and the observations from sample 2 are Yi​, and di=Xi−Yi​, then the null hypothesis is H0​: μd=0 and the alternative hypothesis is H1​: μd ​___ 0.

<

Some have argued that throwing darts at the stock pages to decide which companies to invest in could be a successful​ stock-picking strategy. Suppose a researcher decides to test this theory and randomly chooses 200 companies to invest in. After 1​ year, 104 of the companies were considered​ winners; that​ is, they outperformed other companies in the same investment class. To assess whether the​ dart-picking strategy resulted in a majority of​ winners, the researcher tested H0​: p=0.5 versus H1​: p>0.5 and obtained a​ P-value of 0.2858. Explain what this​ P-value means and write a conclusion for the researcher.​ (Assume α is 0.1 or​ less.)

About 29 in 100 samples will give a sample proportion as high or higher than the one obtained if the population proportion really is 0.5. Because the​ P-value is​ large, do not reject the null hypothesis. There is not sufficient evidence to conclude that the​ dart-picking strategy resulted in a majority of winners.

The headline reporting the results of a poll​ stated, "Majority of Adults at Personal Best in the​ Morning." The results indicated that a survey of 1000 adults resulted in 55​% stating they were at their personal best in the morning. The​ poll's results were reported with a margin of error of 4​%. Explain why the​ poll's headline is accurate.

All the values within the margin of error are greater than​ 50%.

Describe the sampling distribution of p. Assume the size of the population is 25,000. n=200​, p=0.4

Approximately normal because n≤0.05N and np(1-p)>=10

Explain what a​ P-value is. What is the criterion for rejecting the null hypothesis using the​ P-value approach? What is the criterion for rejecting the null hypothesis using the​ P-value approach? Choose the correct answer below.

A​ P-value is the probability of observing a sample statistic as extreme or more extreme than the one observed under the assumption that the statement in the null hypothesis is true. If P-value<α​, reject the null hypothesis.

Twenty years​ ago, 47​% of parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. A recent survey found that 212 of 750 parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. Do parents feel differently today than they did twenty years​ ago? Use the α=0.01 level of significance.

Because np01−p0=186.8186.8greater than>​10, the sample size is less than ​5% of the population​ size, and the sample can be reasonably assumed to be random, the requirements for testing the hypothesis are satisfied. Statcrunch: Proportion stat> one sample> insert all info Since ​P-value<α​, reject the null hypothesis and conclude that there is sufficient evidence that parents feel differently today.

According to a polling​ organization, 21​% of adults in a large region consider themselves to be liberal. A survey asked 200 respondents to disclose their political​ philosophy: Conservative,​ Liberal, Moderate. Treat the results of the survey as a random sample of adults in this region. Do the survey results suggest the proportion is higher than that reported by the polling​ organization? Use an α=0.10 level of significance.

Because np01−p0=33.2>​10; the sample size is less than ​5% of the population​ size, and the sample is given to be random, the requirements for testing the hypothesis are satisfied. Statcrunch: Proportion stat> one sample> insert all info

A professor wanted to determine whether an online homework system improved scores on a final exam. In the fall​ semester, he taught a class using the online homework system​ (which meant students did their homework online and received instant feedback about their answers along with helpful​ guidance). In the spring​ semester, he taught a class without the homework system​ (which meant students were responsible for doing their homework the​ old-fashioned way - paper and​ pencil). The professor made sure to teach the two courses identically​ (same text,​ syllabus, tests, meeting​ time, meeting​ location, and so​ on). The table summarizes the results of the two classes on their final exam. Complete parts ​(a) through ​(e) below.

Completely randomized design Final exam scores Homework system Text, Location, Syllabus, Test, Teacher The assumption is that the students​ "randomly" enrolled in the course. H0: Ufall = Uspring H1: Ufall > Uspring

A sampling method is​ _________ when the individuals selected for one sample are used to determine the individuals in the second sample.

Dependent

The data from a simple random sample with 25 observations was used to construct the plots given below. The normal probability plot that was constructed has a correlation coefficient of 0.946. Judge whether a​ t-interval could be constructed using the data in the sample.

Does not suggest < 0.959 Shows Could not

Suppose there are n independent trials of an experiment with k>3 mutually exclusive​ outcomes, where pi represents the probability of observing the ith outcome. What would be the formula of an expected count in this​ situation?

Ei=npi

True or False When testing a hypothesis using the​ P-value Approach, if the​ P-value is​ large, reject the null hypothesis.

False

True or False Sample evidence can prove that a null hypothesis is true.

False

True or False The population proportion and sample proportion always have the same value.

False

True or False To construct a confidence interval about the​ mean, the population from which the sample is drawn must be approximately normal.

False

In a​ survey, 1400 adults in a certain country were asked how many hours they worked in the previous week. Based on the​ results, a​ 95% confidence interval for mean number of hours worked was lower​ bound: 37.3 and upper​ bound: 45.1. Which of the following represents a reasonable interpretation of the​ result? For those that are not​ reasonable, explain the flaw. Complete parts​ (a) through​ (d) below.

Flawed. This interpretation implies that the population mean varies rather than the interval. Correct. This interpretation is reasonable. Flawed. This interpretation makes an implication about individuals rather than the mean. Flawed. The interpretation should be about the mean number of hours worked by adults in the whole​ country, not about adults in the particular area.

A manufacturer of colored candies states that 13​% of the candies in a bag should be​ brown, 14% ​yellow, 13​% ​red, 24​% ​blue, 20​% ​orange, and 16​% green. A student randomly selected a bag of colored candies. He counted the number of candies of each color and obtained the results shown in the table. Test whether the bag of colored candies follows the distribution stated above at α=0.05 level of significance. Using the level of significance α=0.05​, test whether the color distribution is the same.

H0​: The distribution of colors is the same as stated by the manufacturer. H1​: The distribution of colors is not the same as stated by the manufacturer. Statcrunch: Goodness of fit>Chi-square test>Frequency>Probability

The first significant digit in any number must be​ 1, 2,​ 3, 4,​ 5, 6,​ 7, 8, or 9. It was discovered that first digits do not occur with equal frequency. Probabilities of occurrence to the first digit in a number are shown in the accompanying table. The probability distribution is now known as​ Benford's Law. For​ example, the following distribution represents the first digits in 214 allegedly fraudulent checks written to a bogus company by an employee attempting to embezzle funds from his employer. Complete parts ​(a) and ​(b) below.

H0​: The distribution of the first digits in the allegedly fraudulent checks obeys​ Benford's Law. H1​: The distribution of the first digits in the allegedly fraudulent checks does not obey​ Benford's Law. Statcrunch: Goodness of fit>Chi-square test>Frequency>Probability Yes​, the first digits do not obey ​Benford's Law.

A researcher wanted to determine whether certain accidents were uniformly distributed over the days of the week. The data show the day of the week for n=299 randomly selected accidents. Is there reason to believe that the accidents occur with equal frequency with respect to the day of the week at the α=0.05 level of​ significance?

H0​: p1=p2=...=p7=17 H1​: At least one proportion is different from the others. Statcrunch: Goodness of fit>Chi-square test>all cells in equal proportion

Several years​ ago, the mean height of women 20 years of age or older was 63.7 inches. Suppose that a random sample of 45 women who are 20 years of age or older today results in a mean height of 64.2 inches. ​(a) State the appropriate null and alternative hypotheses to assess whether women are taller today. ​(b) Suppose the​ P-value for this test is 0.07. Explain what this value represents. ​(c) Write a conclusion for this hypothesis test assuming an α=0.05 level of significance.

H0​: μ=63.7 in. versus H1​: μ>63.7 in. There is a 0.07 probability of obtaining a sample mean height of 64.2 inches or taller from a population whose mean height is 63.7 inches. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean height of women 20 years of age or older is greater today.

Explain what ​"95​% ​confidence" means in a 95​% confidence interval.

If 100 different confidence intervals are​ constructed, each based on a different sample of size n from the same​ population, then we expect 95 of the intervals to include the parameter and 5 to not include the parameter.

Suppose a researcher is testing the hypothesis H0​: p=0.3 versus H1​: p≠0.3 and she finds the​ P-value to be 0.22. Explain what this means. Would she reject the null​ hypothesis? Why?

If the​ P-value for a particular test statistic is 0.22​, she expects results at least as extreme as the test statistic in about 22 of 100 samples if the null hypothesis is true. Since this event is not​ unusual, she will not reject the null hypothesis.

In a survey conducted by the Gallup​ Organization, 1100 adult Americans were asked how many hours they worked in the previous week. Based on the​ results, a​ 95% confidence interval for the mean number of hours worked had a lower bound of 42.7 and an upper bound of 44.5. Provide two recommendations for decreasing the margin of error of the interval.

Increase the sample size. Decrease the confidence level.

A sampling method is when an individual selected for one sample does not dictate which individual is to be in the second sample.

Independent

Two​ researchers, Jaime and​ Mariya, are each constructing confidence intervals for the proportion of a population who is​ left-handed. They find the point estimate is 0.15. Each independently constructed a confidence interval based on the point​ estimate, but​ Jaime's interval has a lower bound of 0.071 and an upper bound of 0.187​, while​ Mariya's interval has a lower bound of 0.089 and an upper bound of 0.211. Which interval is​ wrong? Why?

Jaime​'s interval is wrong because it is not centered on the point estimate.

The​ _______ represents the expected proportion of intervals that will contain the parameter if a large number of different samples of size n is obtained. It is denoted​ _______.

Level of confidence (1-a)*100%

Determine whether the following graph can represent a normal density function.

No

A simple random sample of size n=42 is obtained from a population with μ=76 and σ=3. Does the population need to be normally distributed for the sampling distribution of x to be approximately normally​ distributed? Why? What is the sampling distribution of x​?

No because the Central Limit Theorem states that regardless of the shape of the underlying​ population, the sampling distribution of x becomes approximately normal as the sample​ size, n, increases. The sampling distribution of x is normal or approximately normal with μx Statcrunch: Z Stats> One Sample>With summary ux= u ox = statcrunch

A​ _______ is a graph that plots observed data versus normal scores.

Normal probability plot

Suppose a simple random sample of size n=48 is obtained from a population with μ=62 and σ=17. ​(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample​ mean? Assuming the normal model can be​ used, describe the sampling distribution x. ​(b) Assuming the normal model can be​ used, determine ​P(x<66.1​). ​(c) Assuming the normal model can be​ used, determine ​P(x≥63.2​).

Since the sample size is large enough, the population distribution does not need to be normal. IF SAMPLE SIZE NOT LARGE, USE "The population must be normally distributed" Approximately normal, with ux= 62 and ox=17/square 48 ox = Z Stats> One Sample>With summary For P: Statcrunch: Calculator>Normal Use the ox for o!

he standard deviation of the sampling distribution of x​, denoted σx​, is called the​ _____ _____ of the​ _____.

Standard, error, mean.

Use the given statistics to complete parts​ (a) and​ (b). Assume that the populations are normally distributed. ​(a) Test whether μ1>μ2 at the α=0.10 level of significance for the given sample data. ​(b) Construct a 99​% confidence interval about μ1−μ2.

Stat>Tstat>two tests

Use the accompanying data table to ​(a) draw a normal probability​ plot, ​(b) determine the linear correlation between the observed values and the expected​ z-scores, ​(c) determine the critical value in the table of critical values of the correlation coefficient to assess the normality of the data.

Statcrunch: Graph>QQ Plot>Select Columns>Add Correlation statistic Use Critical Values table

A random sample of 16 undergraduate students receiving student loans was​ obtained, and the amounts of their loans for the school year were recorded. Use a normal probability plot to assess whether the sample data could have come from a population that is normally distributed.

Statcrunch: Graph>QQ Plot>Select Columns>Add Correlation statistic Yes. The correlation between the expected​z-scores and the observed data, 0.977 exceeds the critical​ value, 0.941. Therefore, it is reasonable to conclude that the data come from a normal population.

Assume the random variable X is normally distributed with mean μ=50 and standard deviation σ=7. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded.

Statcrunch: Stat>Calculator>Normal

The number of chocolate chips in an​ 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 1252 and standard deviation 129 chips. ​(a) What is the probability that a randomly selected bag contains between 1000 and 1500 chocolate​ chips? ​(b) What is the probability that a randomly selected bag contains fewer than 1050 chocolate​ chips? ​(c) What proportion of bags contains more than 1200 chocolate​ chips? ​(d) What is the percentile rank of a bag that contains 1425 chocolate​ chips?

Statcrunch: Stat>Calculator>Normal (a) Press "Between" Enter 1000 and 1500 = 0.9474 (b) Fewer than is X <= 1050 (c) More than 1200 is X >= 1200 (d) Sign is <= 1425 = 0.9100

The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal​ distribution, with a mean of 17 minutes and a standard deviation of 3 minutes. ​(a) The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does take​ longer, the customer will receive the service for​ half-price. What percent of customers receive the service for​ half-price? ​(b) If the automotive center does not want to give the discount to more than 2​% of its​ customers, how long should it make the guaranteed time​ limit?

Statcrunch: Stat>Calculator>Normal Use >=

Assume the random variable X is normally​ distributed, with mean μ=51 and standard deviation σ=9. Find the 8th percentile.

Statcrunch: Stat>Calculator>Normal Use <= Enter 0.08 into the answer box

Test the hypothesis using the​ P-value approach. Be sure to verify the requirements of the test. H0: p=0.53 versus H1: p<0.53 n=150, x=72, α=0.05

Statcrunch: Proportion stat> one sample> insert all info

Several years​ ago, 45​% of parents who had children in grades​ K-12 were satisfied with the quality of education the students receive. A recent poll asked 1,185 parents who have children in grades​ K-12 if they were satisfied with the quality of education the students receive. Of the 1,185 ​surveyed, 473 indicated that they were satisfied. Construct a 95​% confidence interval to assess whether this represents evidence that​ parents' attitudes toward the quality of education have changed.

Statcrunch: Proportion stat> one sample> insert all info Since the interval does not contain the proportion stated in the null​ hypothesis, there is sufficient evidence that​ parents' attitudes toward the quality of education have changed.

Construct a confidence interval for p1−p2 at the given level of confidence. x1=35​, n1=259​, x2=32​, n2=288​, 95​% confidence

Statcrunch: Proportion stats> two sample> with summary

The table to the right contains observed values and expected values in parentheses for two categorical​ variables, X and​ Y, where variable X has three categories and variable Y has two categories. Use the table to complete parts​ (a) and​ (b) below.

Statcrunch: Tables>Contingency> With summary>select categories H0​: The Y category and X category are independent. H1​: The Y category and X category are dependent.

a​ survey, respondents were asked to disclose their political affiliation​ (Democrat, Independent,​ Republican) and also answer the question​ "Would you be willing to pay higher taxes if the tax revenue went directly toward deficit​ reduction?" Create a contingency table and determine whether the results suggest there is an association between political affiliation and willingness to pay higher taxes to directly reduce the federal debt. Use the α= 0.05 level of significance.

Statcrunch: Tables>Contingency>With Data>select columns>Expected Count

Explain what​ "statistical significance" means.

Statistical significance means that the result observed in a sample is unusual when the null hypothesis is assumed to be true.

Explain the difference between statistical significance and practical significance.

Statistical significance means that the sample statistic is not likely to come from the population whose parameter is stated in the null hypothesis. Practical significance refers to whether the difference between the sample statistic and the parameter stated in the null hypothesis is large enough to be considered important in an application.

Three years​ ago, the mean price of an existing​ single-family home was ​$243,725. A real estate broker believes that existing home prices in her neighborhood are lower. ​(a) Determine the null and alternative hypotheses. ​(b) Explain what it would mean to make a Type I error. ​(c) Explain what it would mean to make a Type II error.

The broker rejects the hypothesis that the mean price is ​$243,725​, when it is the true mean cost. The broker fails to reject the hypothesis that the mean price is ​$243,725​ when the true mean price is less than ​$243725

To test the belief that sons are taller than their​ fathers, a student randomly selects 13 fathers who have adult male children. She records the height of both the father and son in inches and obtains the following data. Are sons taller than their​ fathers? Use the α=0.05 level of significance.​ Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.

The differences are normally distributed or the sample size is large. The sample size is no more than​ 5% of the population size. The sampling method results in a dependent sample. ud = 0 ud < 0 Statcrunch: t-stat>two samples> "<" t= 0.00 Do not reject H0 because the​P-value is greater than the level of significance. There is not sufficient evidence to conclude that sons are taller than their fathers at the 0.025 level of significance.

Suppose the mean IQ score of people in a certain country is 102. Suppose the director of a college obtains a simple random sample of 39 students from that country and finds the mean IQ is 105.6 with a standard deviation of 13.7. Complete parts​ (a) through​ (d) below.

The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually greater than 102. Tstat>one sample> enter = 102 Not reject, accept, accepts, population mean, population mean, does not reject, population mean, population mean, accepting, not rejecting.

A study was conducted that resulted in the following relative frequency histogram. Determine whether or not the histogram indicates that a normal distribution could be used as a model for the variable.

The histogram is not bell-shaped, so a normal distribution could not be used as a model for the variable.

In a survey of 2075 adults in a certain country conducted during a period of economic​ uncertainty, 63​% thought that wages paid to workers in industry were too low. The margin of error was 2 percentage points with 90​% confidence. For parts​ (a) through​ (d) below, which represent a reasonable interpretation of the survey​ results? For those that are not​ reasonable, explain the flaw.

The interpretation is flawed. The interpretation provides no interval about the population proportion. The interpretation is flawed. The interpretation indicates that the level of confidence is varying. The interpretation is reasonable. The interpretation is flawed. The interpretation suggests that this interval sets the standard for all the other​ intervals, which is not true.

A group conducted a poll of 2036 likely voters just prior to an election. The results of the survey indicated that candidate A would receive 46​% of the popular vote and candidate B would receive 45​% of the popular vote. The margin of error was reported to be 2​%. The group reported that the race was too close to call. Use the concept of a confidence interval to explain what this means.

The margin of error suggests candidate A may receive between 44​% and 48​% of the popular vote and candidate B may receive between 43​% and 47​% of the popular vote. Because the poll estimates overlap when accounting for margin of​ error, the poll cannot predict the winner.

Determine the point estimate of the population mean and margin of error for the confidence interval. Lower bound is 17​, upper bound is 25.

The point estimate of the population mean is 21. 17+25=x/2 answer/upper bond

The points at x=​_______ and x=​_______ are the inflection points on the normal curve.

The points are x=μ−σ and x=μ+σ.

For students who first enrolled in two year public institutions in a recent​ semester, the proportion who earned a​ bachelor's degree within six years was 0.393. The president of a certain college believes that the proportion of students who enroll in her institution have a higher completion rate. ​(a) Determine the null and alternative hypotheses. ​(b) Explain what it would mean to make a Type I error. ​(c) Explain what it would mean to make a Type II error.

The president rejects the hypothesis that the proportion of students who earn a​ bachelor's degree within six years is 0.393​, ​when, in​ fact, the proportion is 0.393. The president fails to reject the hypothesis that the proportion of students who earn a​ bachelor's degree within six years is 0.393​, ​when, in​ fact, the proportion is greater than 0.393.

What happens to the probability of making a Type II​ error, β​, as the level of​ significance, α​, ​decreases? Why?

The probability increases. Type I and Type II errors are inversely related.

Find the value of Za

https://www.calculators.org/math/z-critical-value.php

The graph to the right is the uniform probability density function for a friend who is x minutes late. ​(a) Find the probability that the friend is between 25 and 30 minutes late. ​(b) It is 10 A.M. There is a 50​% probability the friend will arrive within how many​ minutes?

The probability that the friend is between 25 and 30 minutes late is 0.167. 1/30*(30-25)=1/6=0.167 There is a 50​% probability the friend will arrive within 15 minutes. 0.5*30=15

According to a​ study, the proportion of people who are satisfied with the way things are going in their lives is 0.72. Suppose that a random sample of 100 people is obtained. Complete parts​ (a) through​ (e) below.

The response is qualitative because the responses can be classified based on the characteristic of being satisfied or not. The sample proportion p is a random variable because the value of p varies from sample to sample. The variability is due to the fact that different people feel differently regarding their satisfaction.

In​ randomized, double-blind clinical trials of a new​ vaccine, children were randomly divided into two groups. Subjects in group 1 received the new vaccine while subjects in group 2 received a control vaccine. After the second​ dose, 114 of 666 subjects in the experimental group​ (group 1) experienced drowsiness as a side effect. After the second​ dose, 71 of 547 of the subjects in the control group​ (group 2) experienced drowsiness as a side effect. Does the evidence suggest that a higher proportion of subjects in group 1 experienced drowsiness as a side effect than subjects in group 2 at the α=0.01 level of​ significance?

The samples are independent. The sample size is less than​ 5% of the population size for each sample. The formula p1 = p2 p1 > p2 Statcrunch: Proportion stats> two sample> with summary If the population proportions are equal, one would expect a sample difference proportion greater than the one observed in about 22 out of 1000 repetitions of this experiment.

A normal score is the expected​ z-score of a data​ value, assuming the distribution of the random variable is normal. Is this statement true or​ false?

The statement is true.

Determine if the following statement is true or false. The normal curve is symmetric about its​ mean, μ.

The statement is true. The normal curve is a symmetric distribution with one​ peak, which means the​ mean, median, and mode are all equal.​ Therefore, the normal curve is symmetric about the​ mean, μ.

According to the Federal Housing Finance​ Board, the mean price of a​ single-family home two years ago was ​$299,800. A real estate broker believes that because of the recent credit​ crunch, the mean price has increased since then. The null hypothesis is rejected.

There is sufficient evidence to conclude that the mean price of a​ single-family home has increased from its level two years ago of ​$299,800

Suppose the null hypothesis is not rejected. State the conclusion based on the results of the test. Three years​ ago, the mean price of a​ single-family home was ​$243,701. A real estate broker believes that the mean price has increased since then.

There is not sufficient evidence to conclude that the mean price of a​ single-family home has increased.

Suppose the null hypothesis is not rejected. State the conclusion based on the results of the test. Six years​ ago, 11.2​% of registered births were to teenage mothers. A sociologist believes that the percentage has increased since then.

There is not sufficient evidence to conclude that the percentage of teenage mothers has increased.

State the conclusion based on the results of the test. According to the​ report, the standard deviation of monthly cell phone bills was ​$48.91 three years ago. A researcher suspects that the standard deviation of monthly cell phone bills is different today. The null hypothesis is not rejected.

There is not sufficient evidence to conclude that the standard deviation of monthly cell phone bills is different from its level three years ago of $48.91.

State the conclusion based on the results of the test. The mean of the pressure required to open a certain valve is known to be μ=7.9 psi. Due to changes in the manufacturing​ process, the​ quality-control manager feels that the average pressure has increased. The null hypothesis was rejected.

There is sufficient evidence that the mean of the pressure required to open a certain valve has increased.

According to a food​ website, the mean consumption of popcorn annually by Americans is 58 quarts. The marketing division of the food website unleashes an aggressive campaign designed to get Americans to consume even more popcorn. Complete parts​ (a) through​ (c) below.

There is sufficient evidence to conclude that the mean consumption of popcorn has risen. The marketing department committed a Type I error because the marketing department rejected the null hypothesis when it was true. The probability of making a Type I error is 0.010.

True or False The mean of the sampling distribution of p is p.

True

True or false The distribution of the sample​ mean, x​, will be normally distributed if the sample is obtained from a population that is normally​ distributed, regardless of the sample size.

True

Determine if the following statement is true or false.​ Why? The expected frequencies in a​ chi-square test for independence are found using the formula below.

True. It is a simplification of multiplying the proportion of a row variable by the proportion of the column variable to find the proportion for a​ cell, then multiplying by the table total.

The null and alternative hypotheses are given. Determine whether the hypothesis test is​ left-tailed, right-tailed, or​ two-tailed. What parameter is being​ tested? H0​: p = 0.5 H1​: p ≠ 0.5

Two Tailed < = left-tailed > = right tailed p = population proportion u = population mean o = population standard deviation

The following data represent the muzzle velocity​ (in feet per​ second) of rounds fired from a​ 155-mm gun. For each​ round, two measurements of the velocity were recorded using two different measuring​ devices, resulting in the following data. Complete parts​ (a) through​ (d) below.

Two measurements​ (A and​ B) are taken on the same round. =0 =/0 T-test>paired> One can be​ 99% confident that the mean difference in measurement lies in the interval found above. ​Yes, because 0 is contained in the boxplot.

The mean waiting time at the​ drive-through of a​ fast-food restaurant from the time an order is placed to the time the order is received is 88.5 seconds. A manager devises a new​ drive-through system that he believes will decrease wait time. As a​ test, he initiates the new system at his restaurant and measures the wait time for 10 randomly selected orders. The wait times are provided in the table to the right. Complete parts​ (a) and​ (b) below.

Yes, are, is, greater u=88.5 u<88.5 Tstat>with data> select column> write 88.5 The​ P-value is less than the level of significance so there is sufficient evidence to conclude the new system is effective.

The notation zα is the​ z-score that the area under the standard normal curve to the right of zα is​ _______.

a

State the requirements to perform a​ goodness-of-fit test.

at least​ 80% of expected frequencies ≥ 5 all expected frequencies ≥ 1

According to the Centers for Disease Control and​ Prevention, 9.6​% of high school students currently use electronic cigarettes. A high school counselor is concerned the use of​ e-cigs at her school is higher. Complete parts​ (a) through​ (c) below.

p = 0.096 p > 0.096 There is not sufficient evidence to conclude that the proportion of high school students exceeds 0.096 at this​ counselor's high school. A Type II error was committed because the sample evidence led the counselor to conclude the proportion of​ e-cig users was 0.096​, ​when, in​ fact, the proportion is higher.

Test the hypothesis using the​ P-value approach. Be sure to verify the requirements of the test. H0: p=0.88 versus H1: p≠0.88 n=500, x=430, α=0.05

p^ = x/n Statcrunch: Proportion stat> one sample> insert all info

A survey​ asked, "How many tattoos do you currently have on your​ body?" Of the 1202 males​ surveyed, 185 responded that they had at least one tattoo. Of the 1060 females​ surveyed, 146 responded that they had at least one tattoo. Construct a 90​% confidence interval to judge whether the proportion of males that have at least one tattoo differs significantly from the proportion of females that have at least one tattoo. Interpret the interval.

proportion stats>two sample>with summary There is 90​% confidence that the difference of the proportions is in the interval. Conclude that there is insufficient evidence of a significant difference in the proportion of males and females that have at least one tattoo

In​ 2003, an organization surveyed 1,508 adult Americans and asked about a certain​ war, "Do you believe the United States made the right or wrong decision to use military​ force?" Of the 1,508 adult Americans​ surveyed, 1,090 stated the United States made the right decision. In​ 2008, the organization asked the same question of 1,508 adult Americans and found that 575 believed the United States made the right decision. Construct and interpret a​ 90% confidence interval for the difference between the two population​ proportions, p2003−p2008.

proportion stats>two sample>with summary There is​ 90% confidence that the difference in the proportion of adult Americans from 2003 to 2008 who believe the United States made the right decision to use military force in the country is between the lower and upper bounds of the interval.

Suppose a simple random sample of size n is drawn from a large population with mean μ and standard deviation σ. The sampling distribution of x has mean μx=​______ and standard deviation σx=​______.

u o/square n

The graph of a normal curve is given. Use the graph to identify the value of μ and σ.

u = 100 (center) o=3 (right of center minus center)

In a​ study, researchers wanted to measure the effect of alcohol on the hippocampal​ region, the portion of the brain responsible for​ long-term memory​ storage, in adolescents. The researchers randomly selected 21 adolescents with alcohol use disorders to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of 9.02 cm3. An analysis of the sample data revealed that the hippocampal volume is approximately normal with no outliers and x=8.03 cm3 and s=0.7 cm3. Conduct the appropriate test at the α=0.01 level of significance.

u = 9.02 u < 9.02 t stat>one sample, summary stats

One​ year, the mean age of an inmate on death row was 41.8 years. A sociologist wondered whether the mean age of a​ death-row inmate has changed since then. She randomly selects 32 ​death-row inmates and finds that their mean age is 41.2​, with a standard deviation of 8.9. Construct a​ 95% confidence interval about the mean age. What does the interval​ imply?

u=41.8 u=/41.8 Since the mean age from the earlier year is contained in the​ interval, there is not sufficient evidence to conclude that the mean age had changed.

Determine μx and σx from the given parameters of the population and sample size.

ux= u ox= statcrunch Statcrunch: Z Stats> One Sample>With summary

In a recent survey​ conducted, a random sample of adults 18 years of age or older living in a certain country were asked their reaction to the word socialism. In​ addition, the individuals were asked to disclose which political party they most associate with. Results of the survey are given in the table. Complete parts ​(a) through ​(c) below.

​H0: pD=pR=pI H1​: At least one of the proportions is different from the others. Statcrunch: Tables>Contingency> With summary>select categories>Column percent ​Yes, there is evidence because the​ P-value is less than a.