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Elementary Statistics A Step By Step Approach 10th Edition Allan G. Bluman - Solutions
According to the almanac, the mean age for a woman giving birth for the first time is 25.2 years. A random sample of ages of 35 professional women giving birth for the first time had a mean of 28.7 years and a standard deviation of 4.6 years. Use both a confidence interval and a hypothesis test at
Using Table G, find the critical value(s) for each. Indicate the noncritical region or regions, and state the null and alternative hypotheses. Use σ2 = 225.a. α = 0.10, n = 14, two-tailedb. α = 0.05, n = 27, right-tailedc. α = 0.01, n = 9, left-tailedd. α = 0.05, n = 17, right-tailed
The average lifetime of circulated $1 bills is 18 months. A researcher believes that the average lifetime is not 18 months. He researched the lifetime of 50 $1 bills and found the average lifetime was 18.8 months. The population standard deviation is 2.8 months. At α = 0.02, can it be concluded
If the variance of the water temperature in a lake is 28°, how many days should the researcher select to measure the temperature to estimate the true mean within 3° with 99% confidence?
According to the World Almanac, 35.2% of men ages 18 to 44 meets the U.S. Fitness Guidelines. How large a sample is necessary to estimate the true proportion of men that are fit in this age group within 2 ½ percentage points with 90% confidence?
The speeds in miles per hour of eight randomly selected qualifiers for the Indianapolis 500 (in 2012) are listed below. Estimate the mean qualifying speed with 95% confidence.Assume that all variables are approximately normally distributed. 224.037 223.422 222.891 226.240 222.929 223.684 226.484
The American Heart Association recommends a daily cholesterol intake of less than 300 mg. Here are the cholesterol amounts in a random sample of single servings of grilled meats. Estimate the standard deviation in cholesterol with 95% confidence. Assume the variable is normally distributed. 90 85
Estimate the standard deviation in calories for these randomly selected standard-size candy bars with 95% confidence. (The number of calories is listed for each.) Assume the variable is normally distributed. 275 260 220 220 210 220 230 280 240 240 240 230 280 260
A recent survey of 349 people ages 18 to 29 found that 86% of them own a smartphone. Find the 99% confidence interval of the population proportion.
What distribution must be used when computing confidence intervals for variances and standard deviations?
For a group of 12 men subjected to a stress test situation, the average heart rate was 109 beats per minute. The standard deviation was 4. Find the 99% confidence interval of the population mean.Assume that all variables are approximately normally distributed.
It is desired to estimate the mean GPA of each undergraduate class at a large university. How large a sample is necessary to estimate the GPA within 0.25 at the 99% confidence level? The population standard deviation is 1.2.
A pizza shop owner wishes to find the 95% confidence interval of the true mean cost of a large cheese pizza. How large should the sample be if she wishes to be accurate to within $0.15? A previous study showed that the standard deviation of the price was $0.26.
A researcher wishes to estimate the average number of minutes per day a person spends on the Internet. How large a sample must she select if she wishes to be 90% confident that the population mean is within 10 minutes of the sample mean? Assume the population standard deviation is 42 minutes.
How large a sample is needed to estimate the population mean for the amount of money a person spends on Christmas presents within $2 and be 95% confident? The standard deviation of the population is $7.50.
A random sample of 36 drivers used on average 749 gallons of gasoline per year. If the standard deviation of the population is 32 gallons, find the 95% confidence interval of the mean for all drivers. If a driver said that he used 803 gallons per year, would you believe that?
The number of grams of carbohydrates in various commercially prepared 7-inch subs is recorded below. The population standard deviation is 6.46. Estimate the mean number of carbs in all similarly sized subs with 95% confidence. 63 55 70 42 51 61 64 67 61 55 56 70 55 57 60 49 58 60 66 55 61 48 56 57
According to a study, 96% of adults ages 18–29 had internet access at home in 2015. A researcher wanted to estimate the proportion of undergraduate college students (18 to 29 years) with access, so she randomly sampled 180 undergraduates and found that 157 had access. Estimate the true proportion
At a large company, the Director of Research found that the average work time lost by employees due to accidents was 98 hours per year. She used a random sample of 18 employees. The standard deviation of the sample was 5.6 hours. Estimate the population mean for the number of hours lost due to
For a random sample of 60 overweight men, the mean of the number of pounds that they were overweight was 30. The standard deviation of the population is 4.2 pounds.a. Find the best point estimate of the average number of excess pounds that they weighed.b. Find the 95% confidence interval of the
A person recently read that 84% of cat owners are women. How large a sample should the person take if she wishes to be 90% confident that her proportion is within 3% of the true population proportion?
A medical researcher surveyed 11 hospitals and found that the standard deviation for the cost for removing a person’s gall bladder was $53. Assume the variable is normally distributed. Based on this, find the 99% confidence interval of the population variance and standard deviation.
A survey of 50 students in grades 4 through 12 found 68% have classroom Wi-Fi access. Find the 99% confidence interval of the population proportion.
A sample of 8 adult elephants had an average weight of 12,300 pounds. The standard deviation for the sample was 22 pounds. Find the 95% confidence interval of the population mean for the weights of adult elephants.Assume that all variables are approximately normally distributed.
A random sample of 50 cars in the drive-thru of a popular fast food restaurant revealed an average bill of $18.21 per car. The population standard deviation is $5.92. Estimate the mean bill for all cars from the drive-thru with 98% confidence.
Since 1975 the average fuel efficiency of U.S. cars and light trucks (SUVs) has increased from 13.5 to 25.8 mpg, an increase of over 90%! A random sample of 40 cars from a large community got a mean mileage of 28.1 mpg per vehicle. The population standard deviation is 4.7 mpg. Estimate the true
In 1960, 67.6% of the U.S. population (aged 14 and over) was married. A random sample of 600 Americans in 2014 indicated that 316 were married. Estimate the true proportion of married Americans with 99% confidence. Assume the variable is normally distributed.
The standard deviation of a sample of 15 automobile repairs at a local garage was $120.82. Assume the variable is normally distributed. Find the 90% confidence of the true variance and standard deviation.
The number of calories per candy bar for a random sample of standard-size candy bars is shown below. Estimate the mean number of calories per candy bar with 98% confidence.Assume that all variables are approximately normally distributed. 220 210 230 220 275 240 220 260 240 240 260 230 280 280
What is necessary to determine the sample size?
In a recent survey of 1000 adults ages 18 to 40, 34% said they had no credit cards. Find the 95% confidence interval of the population proportion.
A manufacturer of pacemakers wants the standard deviation of the lifetimes of the batteries to be less than 1.8 months. A sample of 20 batteries had a standard deviation of 1.6 months. Assume the variable is normally distributed. Find the 95% confidence interval of the standard deviation of the
Research by Steelcase found the average worker get interrupted every 11 minutes and takes 23 minutes to get back on task. From a random sample of 200 workers, 168 said they are interrupted every 11 minutes by email, texts, alerts, etc. Find the 90% confidence interval of the population proportion
The prices (in dollars) for a particular model of digital camera with 18.0 megapixels and a f/3.5−5.6 zoom lens are shown here for 10 randomly selected online retailers. Estimate the true mean price for this particular model with 95% confidence.999 1499 1997 398 591 498 798 849 449 348Assume that
What statistic best estimates μ?
A random sample of 15 registered nurses in a large hospital showed that they worked on average 44.2 hours per week. The standard deviation of the sample was 2.6. Estimate the mean of the population with 90% confidence.Assume that all variables are approximately normally distributed.
What are three properties of a good estimator?
A survey of 100 Americans found that 68% said they find it hard to buy holiday gifts that convey their true feelings. Find the 90% confidence interval of the population proportion.
When should the t distribution be used to find a confidence interval for the mean?
In 2014, six percent of the cars sold had a manual transmission. A random sample of college students who owned cars revealed the following: out of 122 cars, 26 had manual transmissions. Estimate the proportion of college students who drive cars with manual transmissions with 90% confidence.
A researcher wishes to estimate within 2 points the average systolic blood pressure of female college students. If she wishes to be 90% confident, how large a sample should she select if the population standard deviation of female systolic blood pressure is 4.8?
A survey of 1000 U.S. adults found that 33% of people said that they would get no work done on Cyber Monday since they would spend all day shopping online. Find the 95% confidence interval of the true proportion.
What assumption must be made when computing confidence intervals for variances and standard deviations?
Find p̂ and q̂ for each situation.a. n = 60 and X = 35b. n = 95 and X = 43c. 68%d. 55%e. 12%
A survey of 49 individuals found that the average number of times a person blinks his or her eyes is 25 times per minute. Based on this survey, find the 90% confidence of the population mean number of eye blinks per minute. The population standard deviation is 4.
In each case, find p̂ and q̂.a. n = 80 and X = 40b. n = 200 and X = 90c. n = 130 and X = 60d. 25%e. 42%
What is meant by the 95% confidence interval of the mean?
Find the z value that corresponds to the given area. 0.8962
About 12.5% of restaurant bills are incorrect. If 200 bills are selected at random, find the probability that at least 22 will contain an error. Is this likely or unlikely to occur?
Between z = −1.46 and z = −1.77Find the area under the standard normal distribution curve.
The average overseas trip cost is $2708 per visitor. If we assume a normal distribution with a standard deviation of $405, what is the probability that the cost for a randomly selected trip is more than $3000? If we select a random sample of 30 overseas trips and find the mean of the sample, what
For a certain group of individuals, the average heart rate is 72 beats per minute. Assume the variable is normally distributed and the standard deviation is 3 beats per minute. If a subject is selected at random, find the probability that the person has the following heart rate.a. Between 68 and 74
Twenty-two percent of work injuries are back injuries. If 400 work-injured people are selected at random, find the probability that 92 or fewer have back injuries.
Between z = 1.09 and z = 1.83Find the area under the standard normal distribution curve.
According to the World Almanac, 72% of households own smartphones. If a random sample of 180 households is selected, what is the probability that more than 115 but fewer than 125 have a smartphone?
In the second quarter of 2015, the average movie ticket cost $8.61. In a random sample of 50 movie tickets from various areas, what is the probability that the mean cost exceeds $8.00, given that the population standard deviation is $1.39?
The average number of potholes per 10 miles of paved U.S. roads is 130. Assume this variable is approximately normally distributed and has a standard deviation of 5. Find the probability that a randomly selected road hasa. More than 142 potholes per 10 milesb. Less than 125 potholes per milec.
Seventy-six percent of small business owners do not have a college degree. If a random sample of 60 small business owners is selected, find the probability that exactly 48 will not have a college degree.
To the left of z = −1.87Find the area under the standard normal distribution curve.
The average retail price of gasoline (all types) for 2014 was 342 cents. What would the standard deviation have to be in order for there to be a 15% probability that a gallon of gas costs less than $3.00?
The average number of earthquakes that occur in Los Angeles over one month is 36. (Most are undetectable.) Assume the standard deviation is 3.6. If a random sample of 35 months is selected, find the probability that the mean of the sample is between 34 and 37.5.
In a recent year, the rate of U.S. home ownership was 65.9%. Choose a random sample of 120 households across the United States. What is the probability that 65 to 85 (inclusive) of them live in homes that they own?
To the right of z = 0.37Find the area under the standard normal distribution curve.
The average amount a slot machine makes per month is $8000. This is after payouts. Assume the earnings are normally distributed with a standard deviation of $750. Find the amount of earnings if 15% is considered too low.
The average number of moves a person makes in his or her lifetime is 12. If the standard deviation is 3.2, find the probability that the mean of a sample of 36 people isa. Less than 10b. Greater than 10c. Between 11 and 12
The average cost of repairing an smartphone is $120 with a standard deviation of $10.50. The costs are normally distributed. If 15% of the costs are considered excessive, find the cost in dollars that would be considered excessive.
What formula is used to gain information about an individual data value when the variable is normally distributed?
In a recent year, about 22% of Americans 18 years and older are single. What is the probability that in a random sample of 200 Americans 18 or older more than 30 are single?
Between z = 0 and z = 1.93Find the area under the standard normal distribution curve.
The average prison sentence for a person convicted of second-degree murder is 15 years. If the sentences are normally distributed with a standard deviation of 2.1 years, find these probabilities:a. A prison sentence is greater than 18 years.b. A prison sentence is less than 13 years.
The average lifetime of smoke detectors that a company manufactures is 5 years, or 60 months, and the standard deviation is 8 months. Find the probability that a random sample of 30 smoke detectors will have a mean lifetime between 58 and 63 months.
Between z = 0 and z = 1.07Find the area under the standard normal distribution curve.
What are two other names for a normal distribution?
The average salary for graduates entering the actuarial field is $63,000. If the salaries are normally distributed with a standard deviation of $5000, find the probability thata. An individual graduate will have a salary over $68,000.b. A group of nine graduates will have a group average over
What does the central limit theorem say about the shape of the distribution of sample means?
What percentage of the area falls below the mean? Above the mean?
What is the standard deviation of the sample means called? What is the formula for this standard deviation?
Using the standard normal distribution, find each probability.a. P(z > 1.66)b. P(z < −2.03)c. P(z > −1.19)d. P(z < 1.93)e. P(z > −1.77)
What is the total area under the standard normal distribution curve?
What is the mean of the sample means?
Using the standard normal distribution, find each probability.a. P(0 < z < 2.23)b. P(−1.75 < z < 0)c. P(−1.48 < z <1.68)d. P(1.22 < z < 1.77)e. P(−2.31 < z < 0.32)
Why is the standard normal distribution important in statistical analysis?
Why do most of the sample means differ somewhat from the population mean? What is this difference called?
Find the area under the standard normal distribution for each.a. Between z = 1.10 and z = −1.80b. To the right of z = 1.99c. To the right of z = −1.36d. To the left of z = −2.09e. To the left of z = 1.68
If samples of a specific size are selected from a population and the means are computed, what is this distribution of means called?
Find the area under the standard normal distribution curve for each.a. Between z = 0 and z = 2.06b. Between z = 0 and z = 0.53c. Between z = 1.26 and 1.74d. Between z = −1.02 and z = 1.63e. Between z = −0.07 and z = 0.49
A worker in the automobile industry works an average of 43.7 hours per week. If the distribution is approximately normal with a standard deviation of 1.6 hours, what is the probability that a randomly selected automobile worker works less than 40 hours per week?
Find the z value that corresponds to the given area. 0.0188
Find P(z < 2.3 or z > −1.2).
Find P(z > 2.3 and z < −1.2).
Find the equation for the standard normal distribution by substituting 0 for μ and 1 for σ in the equation .-х- р?/2 «3) y: У 3 oV 2л
Find P(−1 < z < 1), P(−2 < z < 2), and P(−3 < z < 3).How do these values compare with the empirical rule?
Find the z value that corresponds to the given area. 0.9671-
Find the z value that corresponds to the given area. 0.0239
Find the z value that corresponds to the given area. 0.4175
Find the probabilities for each, using the standard normal distribution.P(−2.07 < z < 1.88)
If a distribution of raw scores were plotted and then the scores were transformed to z scores, would the shape of the distribution change? Explain your answer.
Consider the distribution of monthly Social Security (OASDI) payments. Assume a normal distribution with a standard deviation of $120. If one-fourth of the payments are above $1255.94, what is the mean monthly payment?
The mean temperature for a July in Pittsburgh is 73°. Assuming a normal distribution, what would the standard deviation have to be if 5% of the days have a temperature of at least 85°?
Find the probabilities for each, using the standard normal distribution.P(z < −1.51)
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