Stats Practice Exam
Find the indicated area under the curve of the standard normal distribution; then convert it to a percentage and fill in the blank. About ______% of the area is between z=−3 and z=3 (or within 3 standard deviations of the mean).
99.73
A survey found that women's heights are normally distributed with mean 62.6 in. and standard deviation 2.5 in. The survey also found that men's heights are normally distributed with mean 68.9 in. and standard deviation 3.6 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 56 in. and a maximum of 62 in. Complete parts (a) and (b) below. a. Find the percentage of men meeting the height requirement. What does the result suggest about the genders of the people who are employed as characters at the amusement park? Since most men _______ the height requirement, it is likely that most of the characters are _________. b. If the height requirements are changed to exclude only the tallest 50% of men and the shortest 5% of men, what are the new height requirements?
A) Enter results in a normal distribution calculator. with min and max, mean and Standard deviation to receive 0.0275 as your answer. Do not meet, Women B) Same deal, enter area in for new exclusion and write your results
The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first determine the percentage of adults who have heard of the brand. How many adults must he survey in order to be 90% confident that his estimate is within six percentage points of the true population percentage? Complete parts (a) through (c) below. A) Assume that nothing is known about the percentage of adults who have heard of the brand. B) Assume that a recent survey suggests that about 77% of adults have heard of the brand. C) Given that the required sample size is relatively small, could he simply survey the adults at the nearest college? A. No, a sample of students at the nearest college is a stratified sample, not a simple random sample, so it is very possible that the results would not be representative of the population of adults. B. Yes, a sample of students at the nearest college is a simple random sample, so the results should be representative of the population of adults. C. No, a sample of students at the nearest college is a cluster sample, not a simple random sample, so it is very possible that the results would not be representative of the population of adults. D. No, a sample of students at the nearest college is a convenience sample, not a simple random sample, so it is very possible that the results would not be representative of the population of adults.
A) Go to the normal calculator dist. on Statcrunch, enter you confidence interval, Multiply by .5*.5 (since we don't know the proportions, we assume 50%) and divide everything over the Margin of error squared. It should look like: n=([zα/2]^2*.25)/E^2 B) Same deal: n=((1.6449)^2*(.77*.23))/(.06)^2 n=134 C) (D) No, a sample of students at the nearest college is a convenience sample, not a simple random sample, so it is very possible that the results would not be representative of the population of adults.
When conducting research on color blindness in males, a researcher forms random groups with five males in each group. The random variable x is the number of males in the group who have a form of color blindness. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied. Does the table show a probability distribution? Select all that apply. A. Yes, the table shows a probability distribution. B. No, the random variable x is categorical instead of numerical. C. No, not every probability is between 0 and 1 inclusive. D. No, the sum of all the probabilities is not equal to 1. E. No, the random variable x's number values are not associated with probabilities. Find the mean of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A) Yes the table shows a probability distribution B) Your equation is going to look like (0*.646)+(1*.297)+(2*.052).....
Which concept below is NOT a main idea of estimating a population proportion? A. Using a sample statistic to estimate the population proportion is utilizing descriptive statistics. B. The sample proportion is the best point estimate of the population proportion. C. We can use a sample proportion to construct a confidence interval to estimate the true value of a population proportion. D. Knowing the sample size necessary to estimate a population proportion is important.
A.) Using a sample statistic to estimate the population proportion is utilizing descriptive statistics.
In a study of the accuracy of fast food drive-through orders, Restaurant A had 321 accurate orders and 51 that were not accurate. a. Construct a 90% confidence interval estimate of the percentage of orders that are not accurate. b. Compare the results from part (a) to this 90% confidence interval for the percentage of orders that are not accurate at Restaurant B: 0.125<p<0.182. What do you conclude?
A: Construct a 90% confidence interval. Express the percentages in decimal form. ___<p<____ B: Since the two confidence intervals overlap, neither restaurant appears to have a significantly different percentage of orders that are not accurate.
Express the confidence interval (0.080,0.142) in the form of p−E<p<p+E.
Answer question like Lower<p<Higher
Refer to the accompanying data set of mean drive-through service times at dinner in seconds at two fast food restaurants. Construct a 99% confidence interval estimate of the mean drive-through service time for Restaurant X at dinner; then do the same for Restaurant Y. Compare the results.
Compare the results, D. The confidence interval estimates for the two restaurants overlap, so there does not appear to be a significant difference between the mean dinner times at the two restaurants.
A _______ random variable has either a finite or a countable number of values.
Discrete
Discrete vs. Continuous Variables
Discrete: A finite number of values between any two values. A discrete variable is always numeric. For example, the number of customer complaints or the number of flaws or defects. Continuous: An infinite number of values between any two values. A continuous variable can be numeric or date/time. For example, the length of a part or the date and time a payment is received.
In a test of the effectiveness of garlic for lowering cholesterol, 49 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes (before−after) in their levels of LDL cholesterol (in mg/dL) have a mean of 4.9 and a standard deviation of 16.2. Construct a 90% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol? What does the confidence interval suggest about the effectiveness of the treatment? A. The confidence interval limits do not contain 0, suggesting that the garlic treatment did not affect the LDL cholesterol levels. B. The confidence interval limits do not contain 0, suggesting that the garlic treatment did affect the LDL cholesterol levels. C. The confidence interval limits contain 0, suggesting that the garlic treatment did not affect the LDL cholesterol levels. D. The confidence interval limits contain 0, suggesting that the garlic treatment did affect the LDL cholesterol levels.
Enter data on Statcrunch using a t distribution (they hint it to you already by allowing you to view the t dist. table). Round as needed. Answer: (B) The confidence interval limits do not contain 0, suggesting that the garlic treatment did affect the LDL cholesterol levels.
Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
Find the area of the non shaded region. Use the formula x=μ+(z*σ)
z distribution vs. t distribution
First, determine if the pop. is greater than 30, if not, signs point to t. If they don't give you sigma (σ), the population standard deviation, it will be a t distribution
Is the square footage of a house a discrete random variable, a continuous random variable, or not a random variable? A. It is a discrete random variable. B. It is a continuous random variable. C. It is not a random variable.
It is a continuous random variable
Determine whether the value is a discrete random variable, continuous random variable, or not a random variable. The distance a baseball travels in the air after being hit
It is a continuous random variable.
Is the number of free-throw attempts before the first shot is made a discrete random variable, a continuous random variable, or not a random variable? A. It is a continuous random variable. B. It is a discrete random variable. C. It is not a random variable.
It is a discrete random variable
Is the number of people with blood type A in a random sample of 13 people a discrete random variable, a continuous random variable, or not a random variable? A. It is a discrete random variable. B. It is a continuous random variable. C. It is not a random variable.
It is a discrete random variable
Is the number of textbook authors now sitting at a computer a discrete random variable, a continuous random variable, or not a random variable? A. It is a discrete random variable. Your answer is correct. B. It is a continuous random variable. C. It is not a random variable
It is a discrete random variable
Is the political party affiliation of adults in the United States a discrete random variable, a continuous random variable, or not a random variable? A. It is a discrete random variable. B. It is a continuous random variable. C. It is not a random variable.
It is not a random variable
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 9minutes. Find the probability that a randomly selected passenger has a waiting time less than 1.75 minutes. Find the probability that a randomly selected passenger has a waiting time less than 1.75 minutes.
Literally, if its uniformly distributed, just divide that shit and get the decimal/percentage value. 1.75/9=.194
Assume that random guesses are made for 4 multiple-choice questions on a test with 5 choices for each question, so that there are n=4 trials, each with probability of success (correct) given by p=0.20. Find the probability of no correct answers.
Since the probability of getting something wrong is .8, raise .8 to the number of trials to receive the probability. .8^4=.410
The normality requirement for a confidence interval estimate of σ is ____ than the normality requirement for a confidence interval estimate of μ. Departures from normality have a ______ effect on confidence interval estimates of σ than on confidence interval estimates of μ. That is, a confidence interval estimate of σ is ____ robust against a departure from normality than a confidence interval estimate of μ.
Stricter, Greater, Less
The value E is
The Margin of error
Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
The area of the shaded region is .5517
Which of the following is NOT a property of the sampling distribution of the sample mean?
The distribution of the sample mean tends to be skewed to the right or left.
What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?
The mean and standard deviation have the values of μ=0 and σ=1
Refer to the accompanying table, which describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Find the mean and standard deviation for the number of girls in 8 births.
The mean is μ= 4.0 The standard deviation is σ=1.4
Which of the following is NOT a property of the chi-square distribution? A. The chi-square distribution is different for each number of degrees of freedom. B. The values of chi-square can be zero or positive, but they cannot be negative. C. The chi-square distribution is not symmetric. D. The mean of the chi-square distribution is 0.
The mean of the chi-square distribution is 0.
Which of the following is NOT a property of the Student t distribution?
The standard deviation of the Student t distribution is s=1.
Refer to the accompanying data display that results from a sample of airport data speeds in Mbps. The results in the screen display are based on a 95% confidence level. Write a statement that correctly interprets the confidence interval.
We have 95% confidence that the limits of 13.05 Mbps and 22.15 Mbps contain the true value of the mean of the population of all data speeds at the airports.
Assume that the readings on the thermometers are normally distributed with a mean of 0° and standard deviation of 1.00°C.Assume 2.8% of the thermometers are rejected because they have readings that are too high and another 2.8% are rejected because they have readings that are too low. Draw a sketch and find the two readings that are cutoff values separating the rejected thermometers from the others.
Which graph represents the region in which thermometers are rejected? Choose the correct graph below: The one with the two other wings shaded The cutoff values are negative −1.91,1.91 degrees.
Determine whether or not the procedure described below results in a binomial distribution. If it is not binomial, identify at least one requirement that is not satisfied. Four hundred different voters in a region with two major political parties, A and B, are randomly selected from the population of 3.4 million registered voters. Each is asked if he or she is a member of political party A, recording Yes or No.
Yes, the result is a binomial probability distribution
A Gallup poll of 1236 adults showed that 12% of the respondents believe that it is bad luck to walk under a ladder. Consider the probability that among 30 randomly selected people from the 1236 who were polled, there are at least 2 who have that belief. Given that the subjects surveyed were selected without replacement, the events are not independent. Can the probability be found by using the binomial probability formula? Why or why not?
Yes. Although the selections are not independent, they can be treated as being independent by applying the 5% guideline.
Refer to the accompanying data display that results from a sample of airport data speeds in Mbps. Complete parts (a) through (c) below. TInterval (13.046,22.15) x=17.598 Sx=16.01712719 n=50 a.Express the confidence interval in the format that uses the "less than" symbol. Given that the original listed data use one decimal place, round the confidence interval limits accordingly. b.Identify the best point estimate of μ and the margin of error. c. In constructing the confidence interval estimate of μ, why is it not necessary to confirm that the sample data appear to be from a population with a normal distribution? A. Because the sample standard deviation is known, the normal distribution can be used to construct the confidence interval. B. Because the population standard deviation is known, the normal distribution can be used to construct the confidence interval. C. Because the sample size of 50 is greater than 30, the distribution of sample means can be treated as a normal distribution. Your answer is correct. D. Because the sample is a random sample, the distribution of sample means can be treated as a normal distribution.
a: take what's in the parentheses, round as needed. Enter as 13.05<μ<22.15 b. Since μ is represented in this problem by x, simply round as needed. For E take the upper limit, subtract from the lower limit, and divide by 2. In this instance, it would be (22.15-13.046)/2 =4.55 c. Evaluate your data to determine the right answer. In this instance, it's C
What conditions would produce a negative z-score?
a z-score corresponding to a value located to the left of the mean
A newspaper provided a "snapshot" illustrating poll results from 1910 professionals who interview job applicants. The illustration showed that 26% of them said the biggest interview turnoff is that the applicant did not make an effort to learn about the job or the company. The margin of error was given as ±3 percentage points. What important feature of the poll was omitted?
c. The confidence level
the value of q^
found from evaluating 1-p^
The value of p^ is
sample proportion
The notation P(z<a) denotes _______.
the probability that the z-score is less than a.
The value of n is
the sample size
The expression zα denotes the z score with an area of α
to its right
If the confidence level is 95%, what is the value of α?
α=.05
What are the values of the mean and standard deviation after converting all pulse rates of women to z scores using z=(x−μ)/σ? The original pulse rates are measure with units of "beats per minute". What are the units of the corresponding z scores? Choose the correct choice below. A.The z scores are measured with units of "beats per minute." B.The z scores are measured with units of "beats." C.The z scores are measured with units of "minutes per beat." D.The z scores are numbers without units of measurement.
μ=0 σ=1 Answer: (D) The z scores are numbers without units of measurement.
