stats test
Which of the following is not a commonly used practice?
. If the distribution of the sample means is normally distributed, and n>30, then the population distribution is normally distributed.
Express the confidence interval (0.063,0.147) in the form of p−E<p<p+E.
0.063<p< 0.147 (Type integers ordecimals.
Which of the following is NOT an equivalent expression for the confidence interval given by 161.7<μ<189.5?
161.7±27.8
Find the critical value zα/2 that corresponds to the given confidence level. 99%
99%: 2.575 95%: 1.96 90%: 1.645
Which of the following is NOT an observation about critical values?
A critical value is the area in the right-tail region of the standard normal curve.
Which of the following would be information in a question asking you to find the area of a region under the standard normal curve as a solution?
A distance on the horizontal axis is given
Which of the following statistics are unbiased estimators of population parameters?
A. Sample proportion used to estimate a population proportion. Your answer is correct. B. Sample variance used to estimate a population variance. E. Sample mean used to estimate a population mean.
Sample data for the arrival delay times (in minutes) of airlines flights is given below. Determine whether they appear to be from a population with a normal distribution. Assume that this requirement is loose in the sense that the population distribution need not be exactly normal, but it must be a distribution that is roughly bell-shaped. LOADING... Click the icon to view the data set. question 7
A. No, because the histogram of the data is not bell shaped, there is more than one outlier, and the points in the normal quantile plot do not lie reasonably close to a straight line
Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value tα/2, (b) find the critical value zα/2, or (c) state that neither the normal distribution nor the t distribution applies. The confidence level is 90%, σ is not known, and the histogram of 58 player salaries (in thousands of dollars) of football players on a team is as shown.
A. 1.67 To determine the critical value tα/2, first determine the value of α for a 99% confidence level. α=0.01 While either technology or a table of critical values of t can be used to determine tα/2 with α=0.01 and n−1=80 degrees of freedom, for this problem, use technology, rounding to two decimal places. tα/2=2.64 Thus, in order to construct a confidence interval for the mean for this sample, the critical value tα/2=2.64 should be used.
Assume a population of 3, 4, and 11. Assume that samples of size n=2 are randomly selected with replacement from the population. Listed below are the nine different samples. Complete parts a through d below. 3,3 3,4 3,11 4,3 4,4 4,11 11,3 11,4 11,11 A. Find the value of the population standard deviation σ. B. Find the standard deviation of each of the nine samples, then summarize the sampling distribution of the standard deviations in the format of a table representing the probability distribution of the distinct standard deviation values. Use ascending order of the sample standard deviations. C. Find the mean of the sampling distribution of the sample standard deviations. D. Do the sample standard deviations target the value of the population standard deviation? In general, do sample standard deviations make good estimators of population standard deviations? Why or why not?
A. 3.559 B. 0. 3/9 .707 2/9 4.95 2/9 5.657 2/9 C. 2.514 D. The sample standard deviations do not target the population standard deviation, therefore, sample standard deviations are biased estimators
. An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 140 lb and 181 lb. The new population of pilots has normally distributed weights with a mean of 148 lb and a standard deviation of 32.1 lb. A. f a pilot is randomly selected, find the probability that his weight is between 140 lb and 181 lb. B. f 34 different pilots are randomly selected, find the probability that their mean weight is between 140 lb and 181 lb. C. When redesigning the ejection seat, which probability is more relevant?
A. Calculator= Second vars, down to normalcdf, enter, lower: 140 upper: 181 U= 148 O= 32.1 paste and .4464, B. U= 148 O= 32.1 N=34 32.1/ square root of 34= 5.5051 (write this down) then Calculator= Second vars, down to normalcdf, enter, lower: 140 upper: 181 U= 148 O= 5.5051 paste and .9269!!!! C. Part (a) because the seat performance for a single pilot is more important.
Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Area= 0.2946
Calculator= Second vars, down to invnormcdf, enter, Area: .2946 U= 0 O= 1 paste and z= -0.54!!
If you select a simple random sample of M&M plain candies and construct a normal quantile plot of their weights, what pattern would you expect in the graphs?
Approximately a straight line.
Which of the following is not true?
A z-score is an area under the normal curve
Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Area= .9738
Calculator= Second vars, down to invnormcdf, enter, Area: .9738 U= 0 O= 1 paste and z= 1.94!!!
Assume that adults have IQ scores that are normally distributed with a mean of μ=100 and a standard deviation σ=20. Find the probability that a randomly selected adult has an IQ less than 136.
Calculator= Second vars, down to normalcdf, enter, lower: -1E99 upper: 136 U= 100 O= 20 paste and .9641!!!
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.
Calculator= Second vars, down to Invenormalcdf, enter, Area= .75 U= 100 O= 15 paste and 110.2!!!
Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Area+ .1788
Calculator= Second vars, down to invnormcdf, enter, Area: .1788 U= 0 O= 1 paste and z= .92!! (to the right of z is positive)
A survey found that women's heights are normally distributed with mean 63.8 in and standard deviation 2.4 in. A branch of the military requires women's heights to be between 58 in and 80 in. a. Find the percentage of women meeting the height requirement. Are many women being denied the opportunity to join this branch of the military because they are too short or too tall? b. If this branch of the military changes the height requirements so that all women are eligible except the shortest 1% and the tallest 2%, what are the new height requirements?
Calculator= Second vars, down to normalcdf, enter, lower: 58 upper: 80 U= 63.8 O= 2.4 paste and .9922, howver it ask for % so its 99.22% and No, because only a small percentage of women are not allowed to join this branch of the military because of their height
Assume that adults have IQ scores that are normally distributed with a mean of μ=105 and a standard deviation σ=15. Find the probability that a randomly selected adult has an IQ between 95 and 115.
Calculator= Second vars, down to normalcdf, enter, lower: 95 upper: 115 U= 105 O= 15 paste and .4950!!!
Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1. z= -.83 z=1.27
Calculator= Second vars, down to normalcdf, enter, lower: -1E99 upper: -.83 U= 0 O= 1 paste and area= .2033 then enter, lower: -1E99 upper: 1.27 U= 0 O= 1 paste and area= .8980 next, subrtact .8980 from .2033 to get .6947!!!
Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. z= 0.44
Calculator= Second vars, down to normalcdf, enter, lower: -1E99 upper: .44 U= 0 O= 1 paste and area= .6700
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. upper limit is 85
Calculator= Second vars, down to normalcdf, enter, lower: -1E99 upper: 85 U= 100 O= 15 paste and .1587!!!
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. 75 to 115 shaded
Calculator= Second vars, down to normalcdf, enter, lower: 75 upper: 115 U= 100 O= 15 paste and .1587!!!
The _______ tells us that for a population with any distribution, the distribution of the sample means approaches a normal distribution as the sample size increases.
Central Limit Theorem
Which of the following is NOT a procedure for determining whether it is reasonable to assume that sample data are from a normally distributed population?
Checking that the probability of an event is 0.05 or less
The _____________ distribution is used to develop confidence interval estimates of variances or standard deviations.
Chi-square
A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment, 21 subjects had a mean wake time of 103.0 min. After treatment, the 21 subjects had a mean wake time of 81.2 min and a standard deviation of 20.8 min. Assume that the 21 sample values appear to be from a normally distributed population and construct a 95% confidence interval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake time of 103.0 min before the treatment? Does the drug appear to be effective?
Construct the 95% confidence interval estimate of the mean wake time for a population with the treatment. 71.771.7 min<μ<90.790.7 min (Round to one decimal place as needed.) What does the result suggest about the mean wake time of 103.0 min before the treatment? Does the drug appear to be effective? The confidence interval does not include the mean wake time of 103.0 min before the treatment, so the means before and after the treatment are different. This result suggests that the drug treatment has a significant effect.
Use the sample data and confidence level given below to complete parts (a) through (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=1067 and x=502 who said "yes." Use a 90% confidence level.
Find the best point estimate of the population proportion p. N: 1067 Confidence level: 90% E: X: 502 O: Calculate: stat, test, down to A:1-Prophzlnt., then put in x:502 n:1067 c level:.0.9 you get (.44534, .49561) p=.4704779756 n=1067 so the population proporion is .470 B. the margin of error is .4705-.4452= .26 C. .445<p<.496 D. One has 90% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion. Your answer is correct. B. 90
Three randomly selected households are surveyed. The numbers of people in the households are 2, 4, and 9. Assume that samples of size n=2 are randomly selected with replacement from the population of 2, 4, and 9. Listed below are the nine different samples. Complete parts (a) through (c). 2,2 2,4 2,9 4,2 4,4 4,9 9,2 9,4 9,9
Find the sample variance for 2, 2. Use the formula below to first solve for the sample mean x, where n is the sample size. x = ∑x/n = 2=2/2 = 2.0 Use the formula below to find each sample variance, where x is the sample mean and n is the sample size. s^2 =∑(x−x)^2/ n−1 or s^2 (2-2.0)^2 + (2-2.0)^2/ (2-1)= 0.00 DO that for each one 0 3/9 2 2/9 12.5 2/9 24.5 2/9 b. Compare the population variance to the mean of the sample variances. Choose the correct answer below. The population variance is equal to the mean of the sample variances. Do the sample variances target the value of the population variance? In general, do sample variances make good estimators of population variances? Why or why not? The sample variances target the population variances, therefore, sample variances make good estimators of population variances.
A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 49.0 and 59.0 minutes. Find the probability that a given class period runs between 51.5 and 51.75 minutes.
First, find the Y. seeing how the graph doesn't start at 0, subtract the lowest value from the highest (59-49= 10) and 1/10= 0.1. Next (51.5-51.75) x(0.1)= (.25)x(0.1)= 0.025
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 5 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 2.25 minutes.
First, you need to find the value of y, which can be found by using the area formula. A=Length x Width. We know the length is 5 and the Area is 1 so we will divide the 1 by 5. the Width= .2. Next, you follow this equation (5-2.25)x (0.2)= (2.75)x(0.2)= =.55 DONE! remember this is a square graph
You are the operations manager for an airline and you are considering a higher fare level for passengers in aisle seats. How many randomly selected air passengers must you survey? Assume that you want to be 99% confident that the sample percentage is within 5.5 percentage points of the true population percentage. Complete parts (a) and (b) below.
Formula is population is unknown n=(zn/z)^2 x .25/ E^2 Formula if pop is known n=(zn/z)^2 x pq/ E^2 mean formula n= (za/2 x O/ E) ^2 z=2.58 e=5.5 so (2.58)^2 x .25/ (.055(because it is percentage points so move the decimal over by 2) ^2 it would be 551 Part B:Assume that a prior survey suggests that about 35% of air passengers prefer an aisle seat. (2.58)^2 x.35 x .65/0.055^2 it would be 501
Which of the following is NOT a property of the chi-square distribution?
The mean of the chi-square distribution is 0.
Which of the following is NOT true in regards to using a normal quantile plot to determine whether or not a distribution is normal? Choose the correct answer below.
If the plot is bell-shaped, the population distribution is normal.
Which of the following is NOT a requirement of constructing a confidence interval estimate for a population variance?
The population must be skewed to the right.
Which of the following is a biased estimator? That is, which of the following does not target the population parameter?
Median
Examine the normal quantile plot and determine whether it depicts sample data from a population with a normal distribution. question 6
No the points do not lie close to a straight line
Use a calculator or computer software to generate a normal quantile plot for the data in the accompanying table. Then determine whether the data come from a normally distributed population.
Question 9 The distribution is normal. The points are reasonably close to a straight line and do not show a systematic pattern that is not a straigh line pattern
The _______ states that if, under a given assumption, the probability of a particular observed event is exceptionally small (such as less than 0.05), we conclude that the assumption is probably not correct.
Rare Event Rule for Inferential Statistics
Which of the following calculations is NOT derived from the confidence interval?
The population mean, μ=(upper confidence limit)+(lower confidence limit) Your answer is correct.
Which of the following is NOT needed to determine the minimum sample size required to estimate a population proportion?
Standard Deviation
Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Draw a graph and find the probability of a bone density test score greater than −1.98.
Starting at -1.98 and shaded to the right. The to find the probability you'll used Normalcdf and enter lower= -1.98 upper= 1E99 U=0 O=1 paste and .9761!!!
When analyzing polls, which of the following is NOT a consideration?
The sample should be a voluntary response or convenience sample.
_____________ is the distribution of all values of the statistic when all possible samples of the same size n are taken from the same population.
The sampling distribution of a statistic
What does it mean to say that the confidence interval methods for the mean are robust against departures from normality?
The confidence interval methods for the mean are robust against departures from normality, meaning they work well with distributions that aren't normal, provided that departures from normality are not too extreme.
_____________ is the distribution of sample proportions, with all samples having the same sample size n taken from the same population.
The sampling distribution of the proportion
The normal quantile plot shown to the right represents duration times (in seconds) of eruptions of a certain geyser from the accompanying data set. Examine the normal quantile plot and determine whether it depicts sample data from a population with a normal distribution. LOADING... Click the icon to view the data set. QUESTION 5
The distribution is not normal. The points are not reasonably close to a straight line.
Use a calculator or computer software to generate a normal quantile plot for the data in the accompanying table. Then determine whether the data come from a normally distributed population. QUestion 10
The distribution is normal. The points are reasonably close to a straight line and do not show a systematic pattern that is not a straight-line pattern.
Which of the following is NOT a property of the sampling distribution of the variance?
The distribution of sample variances tends to be a normal distribution.
Which of the following is NOT a conclusion of the Central Limit Theorem?
The distribution of the sample data will approach a normal distribution as the sample size increases.
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.
Which of the following is NOT a descriptor of a normal distribution of a random variable? Choose the correct answer below.
The graph is centered around 0.
Which of the following is NOT a requirement for a density curve?
The graph is centered around 0.
Which of the following does NOT describe the standard normal distribution?
The graph is uniform.
Assume that thermometer readings are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. For the case below, draw a sketch, and find the probability of the reading. (The given values are in Celsius degrees.) Between 1.50 and 2.25
The graph will be shaded inbetween 1.50 an 2.25. Find the propability by using Normalcdf and enter lower= 1E99 upper= 1,50 U=0 O=1 paste and .9332 then lower= 1E99 upper= 2.25 U=0 O=1 paste and .9878 .9878-.9332= .0546!!!
Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Draw a graph and find the probability of a bone density test score greater than 0.22.
The graph would start at 0.22 and be shaded from there to the right. The to find the probability you'll used Normalcdf and enter lower=0.22 upper= 1E99 U=0 O=1 paste and 0.4129!!!
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 o(standard deviation)=1
Which of the following is NOT required to determine minimum sample size to estimate a population mean?
The size of the population, N
Which of the following is NOT a property of the Student t distribution?
The standard deviation of the Student t distribution is s=1.
Which of the following is NOT a requirement for constructing a confidence interval for estimating the population proportion?
The trials are done without replacement
. An airliner carries 300 passengers and has doors with a height of 76 in. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.8 in. Complete parts (a) through (d). A. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending. B. If half of the 300 passengers are men, find the probability that the mean height of the 150 men is less than 76 in. C. When considering the comfort and safety of passengers, which result is more relevant: the probability from part (a) or the probability from part (b)? Why? D. When considering the comfort and safety of passengers, why are women ignored in this case?
U: 69.0 O: 2.8 N: 150 Calculator= Second vars, down to normalcdf, enter, lower: -1E99 upper: 76 U= 69.0 O= 2.8 paste and .9938 B. O: .2286 Calculator= Second vars, down to normalcdf, enter, lower: -1E99 upper: 76 U= 69.0 O= .2286 paste and 1!! C.The probability from part (a) is more relevant because it shows the proportion of male passengers that will not need to bend D. Since men are generally taller than women, a design that accommodates a suitable proportion of men will necessarily accommodate a greater proportion of women.
Which concept below is NOT a main idea of estimating a population proportion?
Using a sample statistic to estimate the population proportion is utilizing descriptive statistics
Which of the following would be a correct interpretation of a 99% confidence interval such as 4.1<μ<5.6?
We are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of μ.
A food safety guideline is that the mercury in fish should be below 1 part per million (ppm). Listed below are the amounts of mercury (ppm) found in tuna sushi sampled at different stores in a major city. Construct a 90% confidence interval estimate of the mean amount of mercury in the population. Does it appear that there is too much mercury in tuna sushi? 0.55 0.82 0.10 0.98 1.35 0.52 0.85
What is the confidence interval estimate of the population mean μ? . 448.448 ppm<μ<1.0301.030 ppm Yes, because it is possible that the mean is greater than 1 ppm. Also, at least one of the sample values exceeds 1 ppm, so at least some of the fish have too much mercury.
In a test of the effectiveness of garlic for lowering cholesterol, 48 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 3.8 and a standard deviation of 19.1. 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 is the confidence interval estimate of the population mean μ? negative . 83−.83 mg/dL<μ<8.438.43 mg/dL The confidence interval limits contain 0, suggesting that the garlic treatment did not affect the LDL cholesterol levels.
Here are summary statistics for randomly selected weights of newborn girls: n=241, x=29.2 hg, s=7.3 hg. Construct a confidence interval estimate of the mean. Use a 98% confidence level. Are these results very different from the confidence interval 26.9 hg<μ<30.3 hg with only 19 sample values, x=28.6 hg, and s=2.9 hg?
What is the confidence interval for the population mean μ? 28.128.1 hg<μ<30.330.3 hg No, because the confidence interval limits are similar.
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. .97 to the Right of the graph
When it is shaded to the right, you subract the area from 1. so 1-.97= .03 then Calculator= Second vars, down to Invenormalcdf, enter, Area= ..03 U= 100 O= 15 paste and 71.8!!!
Refer to the data set below (body mass index of men) and determine whether the requirement of a normal distribution is satisfied. Assume that this requirement is loose in the sense that the population distribution need not be exactly normal, but it must be a distribution that is basically symmetric with only one mode. 30.8 24.5 26.9 21.5 19.7 32.0 23.7 27.1 26.6 27.7 26.4 25.7 33.5 20.6 22.9 28.1 23.4 25.1 26.1 24.1
Yes. The points in the normal quantile plot lie reasonably close to a straight line
If you are asked to find the 85th percentile, you are being asked to find _____.
a data value associated with an area of 0.85 to its left
Which of the following groups of terms can be used interchangeably when working with normal distributions?
areas, probability, and relative frequencies Your answer is correct.
What conditions would produce a negative z-score?
a z-score corresponding to an area located entirely in the left side of the curve
The number of _______ for a collection of sample data is the number of sample values that can vary after certain restrictions have been imposed on all data values.
degrees of freedom
Finding probabilities associated with distributions that are standard normal distributions is equivalent to _______.
finding the area of the shaded region representing that probability.
Which of the following is NOT true of the confidence level of a confidence interval?
here is a 1−α chance, where α is the complement of the confidence level, that the true value of p will fall in the confidence interval produced from our sample.
A _____________ is a graph of points (x,y) where each x-value is from the original set of sample data, and each y-value is the corresponding z-score that is a quantile value expected from the standard normal distribution.
normal quantile plot
The standard deviation of the distribution of sample means is _______.
o/ the square root of n
Express the confidence interval 0.111<p<0.777 in the form p±E.
p= 0.111 + 0.777/2= .444 E= 0.111- 0.777/2= .333
Fill in the blank. A _______ is a single value used to approximate a population parameter.
point estimate
The _______ is the best point estimate of the population mean.
sample mean
The best point estimate of the population variance σ2 is the _____________.
sample variance s2
Before every flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry 43 passengers, and a flight has fuel and baggage that allows for a total passenger load of 7,224 lb. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than 7,224 lb43=168 lb. What is the probability that the aircraft is overloaded? Should the pilot take any action to correct for an overloaded aircraft? Assume that weights of men are normally distributed with a mean of 178.1 lb and a standard deviation of 37.
sorry babe, try your best 0.9633 Yes. Because the probability is high, the pilot should take action by somehow reducing the weight of the aircraft.
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?
the confidence level
The notation P(z<a) denotes _______.
the probability that the z-score is less than a.
Where would a value separating the top 15% from the other values on the graph of a normal distribution be found?
the right side of the horizontal scale of the graph
A continuous random variable has a _______ distribution if its values are spread evenly over the range of possibilities.
uniform
An IQ test is designed so that the mean is 100 and the standard deviation is 13 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 99% confidence that the sample mean is within 7 IQ points of the true mean. Assume that σ=13 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.
use the mean formula (2.575 x 13/7)^2 equals 22.87, round up because its a human to 23.
A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 360 babies were born, and 324 of them were girls. Use the sample data to construct a 99% confidence interval estimate of the percentage of girls born. Based on the result, does the method appear to be effective?
x:324 n: 360 Calculate: stat, test, down to A:1-Prophzlnt., then put in x:324 n:360 c level:.0.99 you get (.85927, .94073) p=.9 n=360 Yes, the proportion of girls is significantly different from 0.5
A critical value, zα, denotes the _______.
z-score with an area of a to its righ
Which of the following groups has terms that can be used interchangeably with the others?
Percentage, Probability, and Proportion
