STATS Final Review
Measuring the height of a tree is usually more difficult than measuring the diameter of the tree. Therefore, many researchers use regression models to predict the height of a tree from its diameter measured at 4 feet 6 inches from the ground. The following computer output shows the results of a linear regression based on the heights, in feet, and the diameters, in inches, recorded from 31 felled trees.
(0.396, 1.712)
A statistical test involves the following null and alternative hypotheses. H0 :μ=64 Ha :μ>64 Which of the following describes a Type II error?
Failing to reject the null hypothesis when the population mean is greater than 64
Three brands of candy pieces—X, Y, and Z—are made in many colors. Shaela bought one bag of each brand and counted the number of pieces of each color. The graph below shows the relative frequency distribution of colors for each bag. Which of the following statements must be true?
For Brand Y, there were more red candy pieces than green candy pieces in the bag.
Based on the scatterplots, for which gender does there appear to be evidence that the more time a lion cub spends playing, the sooner the cub is likely to begin hunting?
For female cubs only
A randomized block design will be used in an experiment to compare two lotions that protect people from getting sunburned. Which of the following should guide the formation of the blocks?
Participants within each block should be as similar as possible with respect to how easily they get sunburned.
A random variable X has a mean of 120 and a standard deviation of 15. A random variable Y has a mean of 100 and a standard deviation of 9. If X and Y are independent, approximately what is the standard deviation of X - Y ?
17.5
To investigate the relationship between age and preference for two mayoral candidates in an upcoming election, a random sample of city residents was surveyed. The residents were asked which candidate they preferred, and each resident was classified into one of three age-groups. The test statistic for the appropriate hypothesis test was 3.7408. Approximately what is the probability that the observed responses would be as far or farther from the expected responses if there is no association between age-group and preference?
0.1541
The p-value for a one-sided t-test is 0.10. If the test had been two-sided, what would the p-value have been?
0.20
In a large school district, 16 of 85 randomly selected high school seniors play a varsity sport. In the same district, 19 of 67 randomly selected high school juniors play a varsity sport. A 95 percent confidence interval for the difference between the proportion of high school seniors who play a varsity sport in the school district and high school juniors who play a varsity sport in the school district is to be calculated. What is the standard error of the difference?
0.0695
A blind taste test will be conducted with 9 volunteers to determine whether people can taste a difference between bottled water and tap water. Each participant will taste the water from two different glasses and then identify which glass he or she thinks contains the tap water. Assuming that people cannot taste a difference between bottled water and tap water, what is the probability that at least 8 of the 9 participants will correctly identify the tap water?
0.0195
For flights from a particular airport in January, there is a 30 percent chance of a flight being delayed because of icy weather. If a flight is delayed because of icy weather, there is a 10 percent chance the flight will also be delayed because of a mechanical problem. If a flight is not delayed because of icy weather, there is a 5 percent chance that it will be delayed because of a mechanical problem. If one flight is selected at random from the airport in January, what is the probability that the flight selected will have at least one of the two types of delays?
0.335
The probability of obtaining a head when a certain coin is flipped is about 0.65. Which of the following is closest to the probability that heads would be obtained 15 or fewer times when this coin is flipped 25 times?
0.37
A distribution of scores is approximately normal with a mean of 78 and a standard deviation of 8.6. Which of the following equations can be used to find the score x above which 33 percent of the scores fall?
0.44 = (x - 78)/8.6
A die used in a certain board game has eight faces, of which 3 are red, 3 are yellow, and 2 are blue. Each face is equally likely to land faceup when the die is tossed. In the game, a player tosses the die until blue lands faceup, and the number of tosses before blue lands faceup is counted. For example, a player who tosses the sequence shown in the following table has tossed the die 3 times before blue lands faceup. What is the probability that a player will toss the die at least 2 times before blue lands faceup?
0.5625
The table shows the responses from 103 people when asked if they support a proposal to expand the public library. One person from those who responded will be selected at random. Which of the following is closest to the probability that the person selected will be someone who responded no, given that the person selected is age 55 or older?
0.818
The distribution of monthly rent for one-bedroom apartments in a city is approximately normal with mean $936 and standard deviation $61. A graduate student is looking for a one-bedroom apartment and wants to pay no more than $800 in monthly rent. Of the following, which is the best estimate of the percent of one-bedroom apartments in the city with a monthly rent of at most $800 ?
1.3%
A city department of transportation studied traffic congestion on a certain highway. To encourage carpooling, the department will recommend a carpool lane if the average number of people in passenger cars on the highway is less than 2. The probability distribution of the number of people in passenger cars on the highway is shown in the table. Based on the probability distribution, what is the mean number of people in passenger cars on the highway?
1.7
For a particular video game, Ariana's mean number of points earned per game is 190, and the standard deviation is 40. Suppose that she plays 50 games in one evening, and her goal is to obtain a mean score of at least 200 for the 50 games. How many standard deviations above 190 is her goal?
1.77
A news article reported that college students who have part-time jobs work an average of 15 hours per week. The staff of a college newspaper thought that the average might be different from 15 hours per week for their college. Data were collected on the number of hours worked per week for a random sample of students at the college who have part-time jobs. The data were used to test the hypotheses H0: μ = 15 Ha: μ ≠ 15, where µ is the mean number of hours worked per week for all students at the college with part-time jobs. The results of the test are shown in the table below. Assuming all conditions for inference were met, which of the following represents a 95 percent confidence interval for µ?
13.755 ± 1.456
Each accountant at a large accounting firm was classified according to accountant level (junior or senior) and method of transportation to work (walk, bus, drive alone, or carpool). The responses of the 320 accountants at the firm are summarized in the table. What proportion of the accountants at the firm are at the senior level and carpool to work?
20/320
Sophomore, junior, and senior students at a high school will be surveyed regarding a potential increase in the extracurricular student activities fee. There are three possible responses to the survey question - agree with the increase, do not agree with the increase, or no opinion. A chi-square test will be conducted to determine whether the response to this question is independent of the class in which the student is a member. How many degrees of freedom should the chi-square test have?
4
A polling agency conducted a survey about social media in which each person in random samples of 1,000 men and 1,000 women was asked what factor he or she considers to be the most important when deciding whether to connect on social media with another person. The responses are shown in the table.
7.5
Of the homeowners in the sample who have four or more credit cards, what proportion have owned their current homes for at least one year?
78/212
Which of the following is the most appropriate interpretation of the statistic 93.47% in the regression output?
93.47% of the variation in number of runs scored can be explained by the linear regression with OPS.
A town manager is interested in comparing requests for various town-provided services (such as street maintenance and garbage pickup) with nationally published proportions of requests for the same services. Each request in a random sample of 500 service requests from the town was classified into one of 10 different categories. Which of the following tests could be used to determine whether the proportions of service requests classified into the 10 service categories for the town differ from national proportions?
A chi-square goodness-of-fit test
A team of psychologists studied the effect of multitasking on the completion of cognitive tasks. A group of 40 women participated in the study. Each woman owned a smartphone equipped with the same type of keyboard. The women typed a text passage on the phone twice, one time while sitting in a quiet room (a single task) and the other time while walking (a multitask). The order of the single task and the multitask was randomly determined for each woman. The psychologists recorded the time it took each woman to type the text for both tasks. If the conditions of inference are met, which of the following tests is most appropriate to analyze the data?
A matched-pairs t-test for a mean difference
Each voter from a random sample of 334 registered voters was asked their impression of two candidates running for the same national office. The table summarizes the responses.
A one-sample z-interval for estimating a population proportion
Researchers will conduct a study of the television-viewing habits of children. They will select a simple random sample of children and record the number of hours of television the children watch per week. The researchers will report the sample mean as a point estimate for the population mean. Which of the following statements is correct for the sample mean as a point estimator?
A sample of size 25 will produce more variability of the estimator than a sample of size 50.
The transportation department of a large city wants to estimate the proportion of residents who would use a system of aerial gondolas to commute to work. The gondolas would be part of the city's effort to relieve traffic congestion. The department asked a random sample of residents whether they would use the gondolas. The residents could respond with yes, no, or maybe. Which of the following is the best description of the method for data collection used by the department?
A sample survey
A school principal wanted to investigate student opinion about the food served in the school cafeteria. The principal selected at random samples of 50 first-year students, 50 second-year students, 50 third-year students, and 50 fourth-year students to complete a questionnaire. Which of the following best describes the principal's sampling plan?
A stratified random sample
A food scientist conducting a study to investigate the nutritional habits of teenagers in a city selected a random sample of 100 teenagers in the city. Each of the 100 teenagers was asked to complete a survey with questions about age and the number of ounces of carbonated drinks consumed on the previous day. Assuming the conditions for inference have been met, which of the following is an appropriate test and alternative hypothesis to use to investigate whether the average number of ounces of carbonated drinks consumed in a day increases with age for teenagers in the city?
A t-test for the slope of a regression model with alternative hypothesis: Ha : B > 0
Which of the following scatterplots could represent a data set with a correlation coefficient of r = -1?
A.
The distribution of heights of 6-year-old girls is approximately normally distributed with a mean of 46.0 inches and a standard deviation of 2.7 inches. Aliyaah is 6 years old, and her height is 0.96 standard deviation above the mean. Her friend Jayne is also 6 years old and is at the 93rd percentile of the height distribution. At what percentile is Aliyaah's height, and how does her height compare to Jayne's height?
Aliyaah's height is at the 83rd percentile of the distribution, and she is shorter than Jayne.
A florist wanted to investigate whether a new powder added to the water of cut flowers helps to keep the flowers fresh longer than just water alone. For a shipment of roses that was delivered to the store, the florist flipped a coin before placing each rose in its own individual container with water. If the coin landed heads up, the rose was placed in water with the new powder; otherwise, the rose was placed in water alone. Which of the following is the best description of the method used by the florist?
An experiment with a completely randomized design
The distribution of the length of employment for workers at a factory is moderately skewed to the right, with mean 7.4 years and standard deviation 5.6 years. The factory manager will select a random sample of 100 employees to survey. Which of the following best describes the sampling distribution of the sample means of length of employment for samples of size 100?
Approximately normal, with mean 7.4 years and standard deviation less than 5.6 years
To investigate if the distribution has changed, the number of customers who visited the electronics department of the store was recorded for each of 50 randomly selected time periods. The results are shown in the table below.
At the significance level α = 0.05, the data provide convincing evidence that the current distribution is different from the historical distribution.
In a study researching how donating to charity can affect a person's happiness, 96 participants were given $5 a day for one week. Each participant was randomly assigned to one of two groups. Those assigned to the first group were asked to spend the money on themselves, and those assigned to the second group were asked to donate the money to charity. At the end of the week, all of the participants were asked to rate their overall level of happiness on a scale from 0 to 100, with higher scores indicating greater levels of happiness. Which of the following are the appropriate null and alternative hypotheses to test whether the sample data provide convincing statistical evidence that donating to charity results in greater happiness than spending on oneself, on average?
B
According to government data, 22 percent of children in the United States under the age of 6 years live in households with incomes that are classified at a particular income level. A simple random sample of 300 children in the United States under the age of 6 years was selected for a study of learning in early childhood. If the government data are correct, which of the following best approximates the probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level? (Note: z represents a standard normal random variable.)
B.
A biologist wants to estimate the difference between the mean body lengths of green and brown stinkbugs. A random sample of 20 green stinkbugs has a mean body length of 16.22 millimeters (mm) and a standard deviation of 1.34 mm. A random sample of 20 brown stinkbugs has a mean body length of 13.41 mm and a standard deviation of 0.73 mm. What is the standard error of the difference (green - brown) between the sample means?
C
A survey of a random sample of 1,045 young adults found that 60 percent do not have a landline telephone number. A hypothesis test will be used to determine whether the data provide convincing statistical evidence that more than 50 percent of all young adults do not have a landline telephone number. Which of the following is the test statistic for the appropriate test? Responses
C
The management team of a company with 10,000 employees is considering installing charging stations for electric cars in the company parking lots. In a random sample of 500 employees, 15 reported owning an electric car. Which of the following is a 99 percent confidence interval for the proportion of all employees at the company who own an electric car?
C
One point is circled on graph 1. Five points labeled A, B, C, D, and E are identified on graph 2. Which point on graph 2 represents the residual for the circled point on graph 1 ?
C.
The buyer for an electronics store wants to estimate the proportion of defective wireless game controllers in a shipment of 5,000 controllers from the store's primary supplier. The shipment consists of 200 boxes each containing 25 controllers. The buyer numbers the boxes from 1 to 200 and randomly selects six numbers in that range. She then opens the six boxes with the corresponding numbers, examines all 25 controllers in each of these boxes, and determines the proportion of the 150 controllers that are defective. What type of sample is this?
Cluster random sample
A company that sells baby food is interested in the baby food preferences of all families with toddlers from a certain city. A representative from the company sets up a booth at one grocery store in the city that will be used to investigate baby food preference. The representative will ask people with toddlers who walk past the booth to complete the survey. Which of the following best describes the sampling method the company will use?
Convenience sampling
A recent survey concluded that the proportion of American teenagers who have a cell phone is 0.27. The true population proportion of American teenagers who have a cell phone is 0.29. For samples of size 1,000 that are selected at random from this population, what are the mean and standard deviation, respectively, for the sampling distribution of the sample proportion of American teenagers who have a cell phone?
D
A research study indicated a negative linear relationship between two variables: the number of hours per week spent exercising (exercise time) and the number of seconds it takes to run one lap around a track (running time). Computer output from the study is shown below. Assuming that all conditions for inference are met, which of the following is an appropriate test statistic for testing the null hypothesis that the slope of the population regression line equals 0 ?
D
For which of the following scatterplots is the correlation between x and y closest to 0 ?
E.
A well-designed experiment should have which of the following characteristics? I. Subjects assigned randomly to treatments II. A control group or at least two treatment groups III. Replication
I, II and III
An experiment was conducted to investigate whether submersion in cold water causes a lower heart rate. The experiment used 50 volunteers. The 25 youngest volunteers had their heart rate measured while holding their breath for 30 seconds with their face submerged in cold water. The 25 oldest volunteers had their heart rate measured while holding their breath for 30 seconds with their face not submerged in cold water. The mean heart rate for volunteers who had their face submerged in cold water was lower than the mean heart rate for volunteers who did not have their face submerged in cold water. Which of the following elements of a well-designed experiment is missing? 1. Comparison of at least two treatment groups 2. Random assignment of treatments to experimental units 3. Replication
II only
A researcher constructed a 95 percent confidence interval for the mean number of alfalfa weevils on an alfalfa plant within a field. Based on 80 randomly selected alfalfa plants, the researcher found an average of 2.5 alfalfa weevils per plant and computed the 95 percent confidence interval to be 1.50 to 3.50. Which of the following statements is a correct interpretation of the 95 percent confidence level?
If we repeatedly sampled this field, taking samples of 80 plants and constructing 95% confidence intervals, then, approximately 95 percent of these intervals would include the population mean number of alfalfa weevils on an alfalfa plant in this field.
The National Honor Society at Central High School plans to sample a random group of 100 seniors from all high schools in the state in which Central High School is located to determine the average number of hours per week spent on homework. A 95 percent confidence interval for the mean number of hours spent on homework will then be constructed using the sample data. Before selecting the sample, the National Honor Society decides that it wants to decrease the margin of error. Which of the following is the best way to decrease the margin of error?
Increase the sample size
For the population of people in the United States who are at least 18 years of age, approximately 61 percent voted in a recent election. A random sample of 200 people and a random sample of 100 people will be selected from the population. For which sample size is it more likely that greater than 70 percent of the sample voted in the recent election?
It is more likely for a sample of size 100 people, because there is more variability in the sampling distribution for smaller sample sizes.
A representative of a car manufacturer in the United States made the following claim in a news report. Ten years ago, only 53 percent of Americans owned American-made cars, but that figure is significantly higher today. A research group conducted a study to investigate whether the claim was true. The group found that 56 percent of a randomly selected sample of car owners in the United States owned American-made cars. A test of the appropriate hypotheses resulted in a p-value of 0.283. Assuming the conditions for inference were met, is there sufficient evidence to conclude, at the significance level of a = 0.05, that the proportion of all car owners in the United States who own American-made cars has increased from what it was ten years ago?
No, because 0.283 > 0.05.
Based on the results of the simulation, is there convincing statistical evidence at the significance level of 0.05 that the event of Audrey selling at least 7 of the 30 selected tickets is unlikely to have occurred by chance alone?
No, because the simulation suggests that Audrey selling at least 7 of 30 selected tickets would occur about 13.8% of the time.
A 95 percent confidence interval for the difference in the population proportions of United States adults that use television as their preferred platform for obtaining news between 2016 and 2018 (2016 minus 2018) was found to be (-0.02,0.18). Based on the interval, is it reasonable for the researchers to claim that there is convincing statistical evidence that the population proportion of United States adults that use television as their preferred method to obtain news differed between 2016 and 2018 ?
No, because zero is included in the interval there is not convincing statistical evidence that the population proportion differed between 2016 and 2018.
The values 60, 62, and 84 were common to both samples. The three values are identified as outliers with respect to the age-group 20 years to 30 years because they are either 1.5 times the interquartile range (IQR) greater than the upper quartile or 1.5 times the IQR less than the lower quartile. Using the same method for identifying outliers, which of the three values are identified as outliers for the age-group 40 years to 50 years?
Only 60 is identified as an outlier.
A large simple random sample of people aged nineteen to thirty living in the state of Colorado was surveyed to determine which of two MP3 players just developed by a new company was preferred. To which of the following populations can the results of this survey be safely generalized?
Only people aged nineteen to thirty living in the state of Colorado
Events D and E are independent, with P( D ) = 0.6 and P( D and E ) = 0.18. Which of the following is true?
P( D or E ) = 0.72
A veterinarian collected data on the weights of 1,000 cats and dogs treated at a veterinary clinic. The weight of each animal was classified as either healthy, underweight, or overweight. The data are summarized in the table. Based on the data in the table, which of the following is the most appropriate type of graph to visually show whether a relationship exists between the type of animal and the weight classification?
Segmented bar chart
The prices, in thousands of dollars, of the 35 used cars at a certain car dealership are shown in the table below. Which of the following best describes the shape of the distribution of used car prices at the dealership?
Skewed to the right (positively skewed)
Which of the following statistics is defined as the 50th percentile?
The Median
A school is having a contest in which students guess the number of candies in a jar. The student whose guess is closest to the correct number of candies in the jar wins a prize. The number of candies guessed by male and female students is shown in the back-to-back stemplot below.
The distributions of guesses for male and female students are both skewed to the left.
A local real estate magazine used the median instead of the mean when it reported the SAT score of the average student who attends Groveland High School. A graphical display of SAT scores of students who attend Groveland High School indicated that the data were strongly skewed to the right. Which of the following explains why, in this situation, the median is a more accurate indicator of the SAT score of the average student than the mean is?
The mean is affected by the skewness, whereas the median is not.
The figure above summarizes the heights, in centimeters, of approximately 400 pine seedlings six years after they were planted at a center for environmental study. Approximately half of the trees were fertilized yearly, and the remaining trees were never fertilized. Which of the following statements about the medians and interquar
The median for the unfertilized trees is less than the median for the fertilized trees, and the IQR is greater for the unfertilized trees.
A statistics student wants to compare the mean times needed to access flight information for two major airlines. Twenty randomly selected students accessed one airline's Web site, and the time required to locate the flight information using the Web site had a mean of 2.5 minutes and a standard deviation of 0.8 minute. Twenty different randomly selected students accessed the other airline's Web site, and the time required to locate the flight information using the Web site had a mean of 2.1 minutes and a standard deviation of 1.1 minutes. Assuming that the conditions for inference are met, which of the following statements about the p-value obtained from the data and the conclusion of the significance test is true?
The p-value is greater than 0.10; therefore, there is no significant difference in mean search times on the two Web sites.
Suppose a hypothesis test will be used to investigate whether the proportion of United States adults who have been a victim of a cybercrime, such as identity theft, is greater than 0.25. Suppose that the hypothesis test is conducted using a significance level of 0.05 and the power of the test is determined for a specific alternative value using the significance level of 0.05. If the significance level of the hypothesis test is changed to 0.01 and the power of the test is computed for the same alternative value using a significance level of 0.01, which of the following best describes the change(s) to the probability of a Type I error and the power of the test?
The probability of a Type I error would decrease, and the power of the test would decrease.
The following table shows the classification of all 51 dogs from an animal shelter by whether the dogs lived mostly outdoors or mostly indoors before coming to the shelter and whether they tested positive or negative for a certain skin condition.
The probability of selecting a dog that tested positive given that the dog lived mostly outdoors is less than the probability of selecting a dog that tested positive given that the dog lived mostly indoors.
Caleb designed an experiment to investigate whether listening to music or chewing gum affects the time to complete a level of a certain video game. Before the game started, each person in a sample was randomly assigned to either listen to music or not listen to music. Each person was also randomly assigned to either chew gum or not chew gum. At the end of the game, the time to complete the level for each person in the sample was recorded. Which of the following correctly identifies the response variable of the experiment and whether the variable is categorical or quantitative?
The response variable is the time to complete the level and the variable is quantitative.
A university will add fruit juice vending machines to its classroom buildings if the student body president is convinced that more than 20 percent of the students will use them. A random sample of n students will be selected and asked whether or not they would use the vending machines. A large-sample test for proportions at the significance level of α = 0.05 will be performed. The null hypothesis that the proportion of all students who would use the vending machines is 20 percent will be tested against the alternative that more than 20 percent of all students would use them. For which of the following situations would the power of the test be highest?
The sample size is n = 1,000, and 50 percent of all students use the vending machines.
According to data from the United States Elections Project, only 36 percent of eligible voters voted in the 2014 elections. For random samples of size 40, which of the following best describes the sampling distribution of p-hat, the sample proportion of people who voted in the 2014 elections?
The sampling distribution is approximately normal, with mean 0.36 and standard deviation 0.076.
In testing to see whether opinion with respect to the use of instant replay is independent of the category of the person interviewed, a chi-square test statistic of 27.99 and a p-value less than 0.001 were calculated. Which of the following statements is correct?
The small p-value suggests that there is evidence of an association between category and opinion about the use of instant replay.
The tail length of Siberian tigers is approximately normally distributed with a mean of 0.85 meter and a standard deviation of 0.13 meter. Which of the following is the best interpretation of the z-score for a particular Siberian tiger with a tail length of 0.8 meter?
The tiger's tail length is approximately 0.38 standard deviation below the mean.
The director of a marketing department wants to estimate the proportion of people who purchase a certain product online. The director originally planned to obtain a random sample of 2,500 people who purchased the product. However, because of budget concerns, the sample size will be reduced to 1,500 people. Which of the following describes the effect of reducing the number of people in the sample?
The variance of the sampling distribution of the estimator will increase.
The point circled on the scatterplot is considered an influential point. A new least-squares regression line will be calculated with the influential point removed. How will the removal of the influential point affect the new least-squares regression line for the remaining 14 points?
The y-intercept will increase, and the slope will be negative.
From what he can tell from the postmarks on both his and his sister's letters, it appears that it takes longer for Lilly's mail from Japan to reach him in Texas than it does for his letters from Texas to reach her in Japan. When Frank called his post office to ask if there was a reason for this, the postmaster told him that the delivery time of letters in both directions should be the same. Frank and his sister decided to collect data to see if letters from Japan to Texas take longer to be delivered than letters from Texas to Japan. They recorded the delivery time in days. After convincing themselves that the assumptions were reasonable, they performed a two-sample t-test and obtained the following computer output. Using a significance level of 0.05, which of the following statements best describes the conclusion that can be drawn from these data?
There is not convincing evidence that the mean delivery time from Japan to Texas is greater than the mean delivery time from Texas to Japan.
A 95 percent confidence interval for the mean time, in minutes, for a volunteer fire company to respond to emergency incidents is determined to be (2.8, 12.3). Which of the following is the best interpretation of the interval?
We are 95% confident that the mean time for response is between 2.8 minutes and 12.3 minutes.
Meteorologists are interested in the relationship between minimum pressure and maximum wind speed of hurricanes. The minimum pressure, in millibars, and maximum wind speed, in knots, were collected for a random sample of 100 hurricanes from the year 1995 to the year 2012. A regression analysis of maximum wind speed on minimum wind pressure produced a 95 percent confidence interval of (-1.42, -1.20) for the slope of the least-squares regression line. Which statement is a correct interpretation of the interval?
We can be 95% confident that wind speed decreases, on average, between 1.20 knots and 1.42 knots for each millibar increase in minimum pressure.
A state educational agency was concerned that the salaries of public school teachers in one region of the state,region A, were higher than the salaries in another region of the state, region B. The agency took two independent random samples of salaries of public school teachers, one from region A and one from region B. The data are summarized in the table below.
Yes, there is evidence at the significance level of α = 0.05 but not at α = 0.01.
Which of the following pairs of sample size n and population proportion p would produce the greatest standard deviation for the sampling distribution of a sample proportion p̂?
n = 100 and p close to 1/2
A researcher conducted a t-test of the hypotheses H0: mu = 38 versus Ha: mu ≠ 38. The sample mean was 35 and the p-value for the test was 0.0627. What would the p-value have been if the researcher had used Ha: mu < 38 as the alternative hypothesis?
½ (0.0627)