Statistics Questions and Answers

Timothy wants to estimate the mean number of siblings for each student in his school. He records the number of siblings for each 75 randomly selected students in the school. What is the statistic? the 75 randomly selected students the mean number of siblings for all students in the school the mean number of siblings for the randomly selected students the specific number of siblings for each randomly selected student all the students in the school

Nine hundred (900) high school freshmen were randomly selected for a national survey. Among survey participants, the mean grade-point average (GPA) was 2.7, and the standard deviation was 0.4. What is the margin of error, assuming a 95% confidence level? (round to the nearest thousandths place)

A study of homeowners in the 5th congressional district in Maryland found that their annual household incomes are normally distributed with a mean of $41,182 and a standard deviation of $11,990 (based on data from Nielsen Media Research). What percentage of household incomes are between $25,000 and $40,000? 62.5% 53.93% 28.23% 37.22%

A data set of values has a mean of 45 and a standard deviation of 5. The z-score for a point A is 0. The z-score for a point B is 0.2. State the values of point A and point B. Point A = Point B =

The shape of the distribution of the time required to get an oil change at a 10-minute oil-change facility is unknown. However, records indicate that the mean time is 11.1 minutes, and the standard deviation is 4.3 minutes. Complete parts (a) through (c) below. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) To compute probabilities regarding the sample mean using the normal model, what size sample would be required? Choose the required sample size below. O A. Any sample size could be used. OB. The normal model cannot be used if the shape of the distribution is unknown. C. The sample size needs to be less than 30. D. The sample size needs to be greater than 30. (b) What is the probability that a random sample of n = 35 oil changes results in a sample mean time less than 10 minutes? The probability is approximately (Round to four decimal places as needed.) (c) Suppose the manager agrees to pay each employee a $50 bonus if they meet a certain goal. On a typical Saturday, the oil-change facility will perform 35 oil changes between 10 A.M. and 12 P.M. Treating this as a random sample, at what mean oil-change time would there be a 10% chance of being at or below? This will be the goal 'established by the manager. Click to select your answer(s).

The local Art Club has 5 members. Their ages are 19, 25, 30, 63, and 30. Find the mode, mean, and standard deviation. Make sure you label each answer.

Listed below are the measured radiation emissions (in W/kg) corresponding to cell phones: A, B, C, D, E, F, G, H, I, J, and K respectively. The media often present reports about the dangers of cell phone radiation as a cause of cancer. Cell phone radiation must be 1.6 W/kg or less. Find the a. mean, b. median, c. midrange, and d. mode for the data. Also complete part e. 1.42 0.72 0.88 1.05 1.14 0.83 0.26 0.21 1.12 1.44 0.87 a. Find the mean. b. Find the median c. Find the midrange. d. Find the mode.

You decide that you want to make sure your estimate from part a is correct. You go out and gather 10 simple random samples of 25 people in your school and calculate the proportion of students within each sample whose Amazon packages arrive within two business days of ordering. The proportion of customers that receive their packages within two days of ordering are given below. 0.70, 0.75, 0.6, 0.95, 0.90, 0.73, 0.87, 0.86, 0.92, 0.97 a. Explain why all of the sample proportions are not the same. b. Find the average of all 10 proportions above.

Suppose a survey of 500 people age 18 to 34 indicated that 32.2% of them live with one or both of their parents. Construct and interpret a 99% confidence interval to estimate the true proportion of all people age 18 to 34 who live with one or both parents.

Round answer to 4 decimal places. Mr. H is playing the batting game at the local fair. He will have six balls pitched to him. The number of balls he can hit determines the prize he wins. He hits the ball 32% of the time (he misses 68% of the time). a. What is the probability he hits exactly two of the pitched balls? b. What is the probability he hits at most 3 of the pitched balls?

Class Survey A student is running a survey for a class project, which asks fellow high school students "What is your favorite sport?" Which of the following would yield the most accurate/most unbiased sample? He hands out a survey to every 3rd classmate to enter his weight training class He hands out the survey to his friends at lunch He passes out surveys as students enter the next soccer game He prints surveys and gives 2 to each teacher to randomly give to a male and female student in their homeroom.

An insurance company crashed four cars of the same model at 5 miles per hour. The costs of repair for each of the four crashes were $429, $437, $476, and $209. Compute the mean, median, and mode cost of repair. Compute the mean cost of repair. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The mean cost of repair is (Round to the nearest cent as needed.) B. The mean does not exist. Compute the median cost of repair. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The median cost of repair is (Round to the nearest cent as needed.) B. The median does not exist. Compute the mode cost of repair. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The mode cost of repair is (Round to the nearest cent as needed.) B. The mode does not exist.

A random variable X can take on three possible values: -5,0, or 10. Each of these values is associated with the following probabilities: P(X=-5) = P(X= 0) = 0.4 and P(X= 10) = 0.2. What is the variance of X?

Classify the hypothesis test as left-tailed, right- tailed, or two-tailed. At one school, the average amount of time that tenth-graders spend watching television each week is21.6 hours. The principal introduces a campaign to encourage the students to watch less television. One year later, the principal wants to perform a hypothesis test to determine whether the average amount of time spent watching television per week has decreased from the previous mean of 21.6 hours. Right-tailed Two-tailed Left-tailed

Which data set is the farthest from a normal distribution? . 2, 3, 3, 4, 4, 4, 5, 5, 6 3, 4, 5, 6, 6, 7, 7, 7, 8, 8, 9, 10 0.9, 1.0, 1.0, 1.1, 1.1, 1.1, 1.2, 1.2, 1.3 4, 4, 4, 5, 5, 6, 7, 7, 8, 8, 8 2, 4, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 10

Trials in an experiment with a polygraph include 98 results that include 24 cases of wrong results and 74 cases of correct results. Use a 0.05 significance level to test the claim that such polygraph results are correct less than 80% of the time. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial distribution.

A helicopter can hold a maximum of 8 people or 1000 pounds. A group of 7 people want to know if they can take a ride. Which measure of central tendency in relation to the group's weight could you use to determine if the 7 people can ride together? Mean Mode Median Standard Deviation

A genetic experiment involving peas yielded one sample of offspring consisting of 433 green peas and 142 yellow peas. Use a 0.01 significance level to test the claim that under the same circumstances, 25% of offspring peas will be yellow. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method and the normal distribution as an approximation to the binomial distribution.

A large corporation sent out four groups of people to conduct observational studies on the average walt time at four different restaurants in its restaurant group. The restaurants have approximately the same ratings in terms of quality and popularity. In their reports to the company board, each of the four groups described different methods used to conduct their studies, as shown in the table. Which group's method will give the most accurate, unbiased results? Northeast Researchers observed and recorded the average wait times each day between the hours of 8 a.m. and 11 a.m. South Researchers used a phone survey to ask residents of the restaurants' city about the wait times they've experienced. A. B. Northeast C. Midwest D. West Coast South West Coast Researchers surveyed restaurant-goers on their wait times as they left the building over the course of one full business day. Midwest Researchers observed and recorded the average wait times during random time periods over the course of a week.

P-value is the A. probability, when the null hypothesis is false, of obtaining a sample result that is at least as unlikely (or as extreme) as what is observed B. probability, when the null hypothesis is true, of obtaining a sample result that is at least as unlikely (or as extreme) as what is observed C. t test statistic (that is, P-value = t test statistic) D. Both B and C.

Polonium-210 is a radioactive substance with a half-life of 138 days. If a nuclear facility is handling 110 grams of polonium-210, then how many grams of polonium- 210 will be left in 270 days. Round your answer 4 decimal places and remember to use labels.

A scatterplot is used to display data where x is the amount of time, in minutes, one member can tolera sauna, and y is the temperature, in degrees Fahrenheit, of the sauna. Which interpretation describes a line of best fit of y=-1.5x + 173 for the data? The member can tolerate a temperature of 173° Fahrenheit for 0 minutes. The amount of time the member can tolerate the heat in a sauna is 173 minutes. The time increased 1.5 minutes for every degree Fahrenheit the temperature increased. The time decreased 1.5 minutes for every degree Fahrenheit the temperature decreased.

A travel association claims that the mean daily meal cost for two adults traveigling together on vacation in San francisco is $105. A random sample of 20 such couples has a mean daily meal cost of $110 and a standard deviation of $8.50. At the α = .05 significance level, is there enough evidence to reject the claim? There is significant evidence that the claim is false, because p = .0165. There is not significant evidence to refute the athletic association's claim because 2.63 is not in the rejection region. Since p = 0.0165, there is evidence that the association's claim is true. No answer text provided.

The mean of the deviations can not be a measure of dispersion because _________ if a data point is less than the mean X, then the deviation is negative if the data points are more consistent, then it is smaller it is always 0 the sum of the deviations is negative

A college believes that 26% of applicants to that school have parents who have remarried. How large a sample is needed to estimate the true proportion of students who have parents who have remarried to within 3% with 99% confidence? 473 2129 2413 1419

Which of the following is true? It is never good to have sampling bias. Statistics are not used to help understand the data collected. A random sample includes only specific people. The best results come from sampling bias.

You conduct a statistical test of hypotheses and find that your data are statistically significant at a = 0.05. In other words, your P-value is equal to or smaller than 0.05. Does it imply that your data are also statistically significant at α = = 0.01? a. Yes b. No c. Cannot be determined

Compute the critical value Za/2 that corresponds to a 85% level of confidence. Click here to view the standard normal distribution table (page 1) Click here to view the standard normal distribution table (page 2). (Round to two decimal places as needed.)

The selling price of a refrigerator, is $601.65. If the markup is 5% of the dealer's cost, what is the dealer's cost of the refrigerator?

Mike wants to find the confidence interval for a set of data. He knows the sample size and the sample proportion. Which other piece of Information does he need to determine the confidence interval? A. the critical value B. the standard deviation C. the number of favorable responses D. the standard error of the mean

In order to predict y-values using the equation of a regression line, what must be true about the correlation coefficient of the variables? Choose the correct answer below. A. The correlation between variables must be significant. B. The correlation between variables must be a y-value of a point on the graph. C. The correlation between variables must be greater than zero. D. The correlation between variables must be an x-value of a point on the graph.

We wish to test the claim that u > 32 at a level of significance of a = 0.05. The sample statistics are n = 50, and x-bar = 32.3. Moreover, it is known that the population standard deviation is a = 12. Compute the test statistic, rounded to two decimal places. 2.31 3.11 1.77 0.98

Assume that a hypothesis test will be conducted using a significance level of a = 0.01 and null hypothesis Ho: μ = 21. Furthermore, assume that the following sample data will be used: n = 12, x-bar = 22.2, and s = 2.1 Find the p-value for the test. 0.9227 0.0478 0.0733 0.1466

A manufacturer claims that fewer than 6% of its fax machines are defective. To test this claim, he selects a random sample of 97 such fax machines and finds that 5% are defective. Find the P-value for the test of the manufacturer's claim. 0.1591 0.3264 0.1736 0.3630

Thirty students raised money by selling frozen pizzas. In total, 400 pizzas were sold. The teacher wants to raffle off a prize proportional to the number of pizzas each student sold. Describe a process that the teacher can use.

In a board game, players take turns spinning a wheel with four spaces and values of $100, $300, $400, $800. The probability of landing on $100 is 4/9. The probability of landing on $300 is 2/9. The probability of landing on $400 is 2/9. The probability of landing on $800 is 1/9. What is the expected value of spinning the wheel once?

The unemployment rate in a city is 14%. If 7 people from the city are sampled at random, find the probability that fewer than 3 of them are unemployed. Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places. (If necessary, consult a list of formulas.)

There were approximately 6.08 billion people in the world in the year 2000. The population grew about 1.23% each year since. Write an exponential function and use it to estimate the world population today.

Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. r = 0.539, n = 25 Critical values: r = 0.487, no significant linear correlation Critical values: r = 0.396, significant linear correlation Critical values: r = 0.487, significant linear correlation Critical values: r = 0.396, no significant linear correlation

The mean weight of a box of cereal filled by a machine is 16.0 ounces, with a standard deviation of 0.3 ounce. If the weights of all the boxes filled by the machine are normally distributed, what percent of the boxes will weigh less than 15.5 ounces? Type or write all your computations to support the answer Round your answer to 0.01%, for example, 22.22%

For the values 1.2, 3, 4, 1.2, 3.2, 4.1, 1.2, 9, 6, 1.2, and 4.5, how much does the standard deviation change if the outlier 9 is removed from the data? attach files

24. Consider the following statements. (i) If u and v are orthogonal in R³ then ||u + v|| = ||u – v|| (ii) ||u||²+ ||v||²||u+v||²+ ||uv||² for all u, v in R³. Which of the above statements is always true? (a) neither (b) (i) only (c) (ii) only (d) (i) and (ii)

A restaurant owner wants to determine the effectiveness of his servers. The owner places a survey regarding the servers' effectiveness with randomly selected customer bills. What is the sample? A. The sample is the servers. B. The sample is all customers of the restaurant. C The sample is the owner of the restaurant. D. The sample is the randomly selected customers.

Select the correct answer. As the number of samples increases, which value can be used to approximate a population mean? A the mean of the sample means B. the standard error of the mean C the confidence interval D. the standard deviation

The average driver spends $54 at the gas station each week with a standard deviation of $8. Assuming that the amount a driver spends on gas follows a normal distribution, solve for the percentage of drivers who spend: 1. More than $40? 2. Less than $30? 3. Between $30 and $40 Include your work with your answer to receive full credit.

Use the probability distribution to complete parts (a) and (b) below. The number of defects per 1000 machine parts inspected Defects Probability 0.260 0.291 0.240 0.155 0.044 (a) Find the mean, variance, and standard deviation of the probability distribution. The mean is

Find the standardized test statistic t for a sample with n = 12, x-bar = 18.8, and s = 2.1. Assume that the significance level is a = .01 and the alternative hypothesis is Ha: m : ≠ 19.3. -0.008 -0.037 -0.381 -0.825

An airline claims that the no-show rate for passengers booked on its flights is less than 6%. Of 380 randomly selected reservations, 18 were no-shows. Assuming that this data is used to test the airline's claim, find the P-value for the test. 0.1499 0.1230 0.3508 0.0746

Which statement is true? A. A sample statistic can never be equal to the population parameter. B. Point estimates are defined for both samples and populations. C To calculate a sample proportion, we need to know the population size. D. To calculate a point estimate, we need to know the sample size.

Suppose you pay $1.00 to roll a fair die with the understanding that you will get $3.00 back for rolling a 4 or a 2, and nothing otherwise. What is the expected amount you will win? - $1.00 $0.00 $3.00 $0.33 $1.00