ANIMSCI 2600 Midterm 2

Suppose x has a binomial probability distribution with n = 400 and p = 0.70. Use the normal approximation to the binomial to find P (X > 300).

0.0166

Suppose x has a binomial distribution with n = 100 and p = 0.60. Use the normal approximation to the binomial to find P(X > 70).

0.0262

Assume that 15% of all pigs die between birth and weaning. In a random sample of 200 births, let X be the number of pigs that die between birth and weaning. Using the normal approximation to the binomial, find the approximate probability that the number of pigs in the sample of 200 that die between birth and weaning is greater than or equal to 40.

0.0301

Find the probability of an observation lying more than z = 1.77 standard deviations above the mean.

0.0384

A population of turkeys has a mean weight of 20 lb and a standard deviation of the weights equal to 4 lb. A turkey breeder selects a large number of samples of 36 turkeys each, calculates the mean weight of the turkeys in each of these samples, and then graphs the sample means. The mean of these sample means is expected to be equal to _______.

20 lb

A Gallop poll is conducted to estimate the proportion of voters who plan to vote in favor of a certain issue on the ballot. A random sample of 500 people of voting age is selected. Results of the poll show that 300 of the 500 people polled plan to vote in favor of the issue. What is the point estimate of the true population proportion of people who plan to vote in favor of the issue?

0.60

A scientist wants to estimate the proportion of mares that conceive when bred by artificial insemination (AI). She selects a random sample of 500 mares and finds that 300 of the 500 mares conceived when bred by AI. What is the point estimate of the true population proportion of mares who become pregnant when bred by AI?

0.60

The average height of a certain ornamental plant is 15 inches and the standard deviation of the heights is 3 inches. Find the probability that a randomly selected plant will have a height between 9 and 18 inches.

0.8185

The average height of a herd of cows is 50 inches and the standard deviation of the heights is 5 inches. Find the probability that a randomly selected cow will have a height between 44 and 58 inches.

0.8301

Find the area under the normal curve between z = -1.25 and z = 1.75.

0.8543

The amount of corn chips dispensed into a 10 ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 10.5 ounces and a standard deviation of 0.2 ounces. What portion of the 10 ounce bags would be expected to contain more than the advertised 10 ounces of corn chips?

0.9938

Assume that the mean length of time required to complete the Columbus Marathon was 4.5 hours and that the standard deviation of the times was 0.50 hours. Assume that the racing times were approximately normally distributed. Only 10% of the runners would be expected to complete the race in less than x hours. Find the value of x.

3.86 hours

The general rule of thumb is that we need a sample size of n > _________ to use large-sample confidence interval procedures to estimate the population mean.

30

A college professor wants to estimate the difference in mean test scores of students who have taken his statistics and genetics classes in the past 10 years. He selects a random sample of 20 student records from the statistics course and a random sample of 22 student records from the genetics course. These two samples were independent random samples. The study provided the results shown in the table below. Calculate the pooled estimate of the variance. Statistics Genetics Sample size 20 22 Sample mean 78 75 Sample standard dev. 10 12

123.10

A population of rabbits has a mean weight of 12 lb with a standard deviation of 3 lb. A rabbit breeder selects 1,000 samples of 36 rabbits each from this population, calculates the mean weight of the rabbits in each of these 1,000 samples, and then graphs the 1,000 sample means. The mean of these 1,000 sample means is expected to be equal to:

12 lb

The average height of a certain ornamental plant is 14 inches and the standard deviation of the heights is 2 inches. Only 20% of the plants are expected to be less than X inches tall. Find the value of X.

12.32 inches

A scientist wants to estimate the true population proportion of mares that conceive when bred by AI. She selects a random sample of 500 mares and finds that 300 of the 500 mares conceived when bred by AI. The scientist knows that it is appropriate to construct a large-sample confidence interval for the true population proportion because

both 0.5343 and 0.6657 lie between 0 and 1.0

Assume that we have a herd of 50 horses and that we want to select a random sample of 5 of the horses for an experiment. We use row 8 of a random number table and go from left to right across the row of random numbers: 96301 91977 05463 07972 18876 20922 94595 56869 69014 60045 18425 84903 42508 32307 Which 5 horses do we include in our random sample ?

horses number: 05 07 18 20 42

Suppose that an 85% confidence interval for μ turns out to be (100 lb, 500 lb). To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. What action should we take to reduce the width of the confidence interval?

increase the sample size

Suppose that a random sample of 256 measurements is selected from a population with a mean of 50 lb and a variance of 16 lb2. What is the mean and standard deviation of the sampling distribution of the sample mean?

mean = 50 lb and standard deviation = 0.25 lb

The Central Limit Theorem states: Consider a random sample of n observations selected from any population with mean μ and standard deviation σ. If the sample size is sufficiently large, then the sampling distribution of the sample mean (X-bar) will be approximately a normal distribution with mean ________ and standard deviation _______.

mean µ and standard deviation σ/√n

The __________ __________ of a statistic is the relative frequency distribution of the values of the statistic theoretically generated by taking repeated random samples of size n and computing the value of the statistic for each sample.

sampling distribution

We randomly select 100,000 samples of size n from a population. We calculate the sample mean (X-bar) for each of the 100,000 random samples and graph the relative frequency distribution for these 100,000 values of X-bar. This relative frequency distribution is called the ____________________ of X-bar.

sampling distribution

The probability of making a Type I error in hypothesis testing is called the __________________ for a hypothesis test.

significance level

The American Angus Association wants to determine the proportion of their members who breed their cows using artificial insemination (AI). They randomly sample 200 of their members and ask them whether or not they breed their cows using AI. 120 of the 200 members sampled said "yes". The proportion of the 200 members who breed their cows using AI is an example of a ____________.

statistic

A researcher wants to determine whether men's and women's attitudes regarding environmental issues differ. Therefore, the researcher samples 100 men and 100 women and asks "Do you think the environment is a major concern"? Of those sampled, 67 women and 53 men responded that they believe that environmental issues are a major concern. What criterion is used to assess whether the Central Limit Theorem can be applied to this problem?

the interval, p-hat + 3 √(p-hat)(q-hat)/n, falls between 0 and 1 for both the men and the women.

We are interested in comparing the mean supermarket prices of two leading colas in the Columbus area. Assume that we have independent random samples of prices of six-packs at 8 supermarkets. The data are shown in the following table: Supermarket Brand 1 Brand 2 1 $2.25 $2.30 2 2.47 2.45 3 2.38 2.44 4 2.27 2.29 5 2.15 2.25 6 2.25 2.25 7 2.36 2.42 8 2.37 2.40 _______________________________________ Mean $2.3125 $2.3500 Standard deviation $0.1007 $0.0859 _______________________________________ Find a 98% confidence interval for the difference in mean price of Brand 1 and Brand 2, assuming that these are independent random samples.

($-0.08529, $0.16029)

You are interested in purchasing a new car. One of the many points you wish to consider is the resale value of the car after 5 years of ownership. Since you are particulary interested in a certain foreign sedan, you decide to estimate the resale value of this car with a 95% confidence interval. You manage to obtain data on 16 recently resold 5-year-old foreign sedans of that model. These 16 cars were resold at an average price of $10,000 with a standard deviation of $1,000. Estimate the true mean resale value of this model of foreign car using a 95% confidence interval.

($9,467.25, $10,532.75)

Scientists want to estimate the difference in twinning rate of two lines of beef cattle that have been selected for increased frequency of twin births. Last spring, 40 of the 100 cows in Line 1 gave birth to twins. In Line 2, 30 of the 100 cows gave birth to twins. Construct a 90% confidence interval for the true difference in population proportions of cows giving birth to twins in Lines 1 and 2. In the interest of time, you can assume that the sample sizes are large enough that it is appropriate to use a large-sample confidence interval.

(-0.01035, 0.21035)

A study published in The Journal of American Academy of Business examined whether the perception of service quality at five-star hotels in Jamaica differs by gender. In order to compare the means of two populations (i.e., male vs. female guests), independent random samples were selected from each population, with the results shown in the table below. Use these data to construct a 96% confidence interval for the difference in the two population means. Males Females Sample size 130 115 Sample mean score 39.10 38.70 Sample standard deviation 6.70 6.95

(-1.393404, 2.193404)

A college professor wants to estimate the difference in mean test scores of students who have taken his statistics and genetics classes in the past 10 years. He selects a random sample of 20 student records from the statistics course and a random sample of 22 student records from the genetics course. These two samples were independent random samples. The study provided the results shown in the table below. Construct a 95% confidence interval for the true difference in population means of these two populations of students. Statistics Genetics Sample size 20 22 Sample mean 78 75 Sample standard dev. 10 12

(-3.92777, 9.92777)

The American Journal of Orthopsychiatry published an article on the prevalence of homelessness in the United States. A sample of 500 adults was asked to respond to the question: "Was there ever a time in your life when you did not have a place to live"? A total of 30 adults in the sample answered yes to this question. Construct a 95% confidence interval to estimate the true population proportion of U.S. adults who have been homeless at some time in their life.

(0.03918, 0.08082)

A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. The dean performs the calculations needed to find a 90% large-sample confidence interval for the true population proportion. Which one of the following confidence intervals is correct?

(0.533, 0.647)

A scientist wants to estimate the true population proportion of mares who conceive when bred by AI. She randomly selects 500 mares and finds that 300 of them became pregnant when bred by AI. Which one of the following is the correct 99% confidence interval for the true population proportion of mares that conceived when bred by AI?

(0.5436, 0.6564)

In order to compare the means of two populations, independent random samples of 400 observations are selected from each population, with the following results: Sample 1 Sample 2 Sample size 400 400 Sample mean 5,275 5,240 Sample standard deviation 150 200 Which one of the following is the correct 92% confidence interval for the difference in the two population means?

(13.125, 56.875)

Toyota would like to know how many miles per gallon the average driver gets when driving the hybrid Toyota Prius. A random sample of 225 drivers yields a mean of 50 mpg and a standard deviation of 7.5 mpg. Estimate the population mean for the miles per gallon of the Prius using a 90% confidence interval. 50 mpg

(49.1775 mpg, 50.8225 mpg)

A beef cattle nutritionist wants to compare the birth weights of calves from cows that receive two different diets during gestation. He therefore selects 16 pairs of cows, where the cows within each pair have similar characteristics. One cow within each pair is randomly assigned to diet 1, while the other cow in the pair is assigned to diet 2. He obtains the following results: Mean difference in birth weights of the pairs of calves = 10 lb Standard deviation of the difference in birth weights of the pairs = 8.0 lb Construct a 95% confidence interval for the true mean difference in birth weights of the calves from cows receiving diet 1 vs. diet 2.

(5.738 lb, 14.262 lb)

The average height of a certain ornamental plant is 15 inches and the standard deviation of the heights is 3 inches. Find the probability that a randomly selected plant will have a height of more than 18.75 inches.

0.1056

The mean length of time required to complete the Columbus Marathon was 4.5 hours. The standard deviation of the times was 0.50 hours. Assume that the racing times were approximately normally distributed. What proportion of the runners would be expected to require between 5.0 and 5.5 hours to complete the race?

0.1359

A population of rabbits has a mean weight of 10 lb and a standard deviation of the weights equal to 2 lb. A rabbit breeder selects 5,000 samples of 64 rabbits each, calculates the mean weight of the rabbits in each of these 5,000 samples, and then graphs the 5,000 sample means. The standard deviation of these 5,000 sample means is expected to be equal to _______.

0.25 lb

Toyota would like to know how many miles per gallon the average driver gets when driving the hybrid Toyota Prius. A random sample of 225 drivers yields a mean of 50 mpg and a standard deviation of 7.5 mpg. Estimate the population mean for the miles per gallon of the Prius using a point estimate.

50 mpg

Suppose we have a population of horses with a mean weight of 1,000 lb and a standard deviation of 50 lb. If we were to take repeated random samples of size n = 100 from the population, the mean and standard deviation, respectively, of the sampling distribution of the sample mean would be:

1,000 lb and 5 lb

A population of rabbits has a mean weight of 10 lb and a standard deviation of the weights equal to 2 lb. A rabbit breeder selects 5,000 samples of 64 rabbits each, calculates the mean weight of the rabbits in each of these 5,000 samples, and then graphs the 5,000 sample means. The mean of these 5,000 sample means is expected to be equal to _______.

10 lb

The average weight of a kennel of dogs is 40 lb and the standard deviation of the weights is 5 lb. Only 14% of the dogs are expected to weigh less than X lb. Find the value of X.

34.6 lb

Assume that we have a herd of 50 horses and that we want to select a random sample of 5 of the horses for an experiment. We begin at row 5 column 1 of a random number table and observe the random numbers shown in the table below. Col. 1 2 3 4 5 6 Row 5: 37570 39975 81837 16656 06121 91782 6: 77921 06907 11008 42751 27756 53498 Which one of the following is the correct set of 5 randomly selected horses to include in our experiment, assuming that we go from left to right across the rows of random numbers?

37 39 16 06 11

The average height cows of a certain breed is 54 inches and the standard deviation of the heights is 8 inches. Fifteen percent of the cows are expected to be less than X inches tall. Find the value of X.

45.68 inches

Which of the following is not one of the properties of the sampling distribution of the sample mean?

All of the above are properties of the sampling distribution of the sample mean.

We want to test the hypothesis that the mean yield of a particular variety of corn is less than 150 bushels per acre. Therefore, we obtain the yields of a random sample of 20 corn fields in which this variety was planted. The average yield of the sample of fields was 140 bushels per acre with a standard deviation of 10 bushels per acre. We want to test: Ho: μ = 150 bushels/acre Ha: μ < 150 bushels/acre using a significance level (α) = 0.10. Should we reject or not reject the null hypothesis? Why?

Because the calculated value of the test statistic (t = -4.47) falls in the lower rejection region below the critical value (t = -1.328), we reject the null hypothesis at α = 0.10.

An assumption required for small-sample estimation of (μ1 - μ2) is that the variances of the samples selected from the two populations are equal.

False

As the sample size (n) increases, the variation in the sampling distribution of the sample means increases.

False

For a fixed confidence coefficient, the width of the confidence interval increases as the sample size increases.

False

It would be appropriate to construct a large-sample confidence interval for (p1 - p2) as long as both n1 and n2 are ≥ 30.

False

The Central Limit Theorem guarantees that the population is normally distributed whenever n is sufficiently large (n > 30).

False

The standard deviation of the sampling distribution of the sample mean is equal to σ, the standard deviation of the population.

False

A sales representative for a seedcorn company tells his boss that within the past year he has contacted 80% of the farmers in his sales district. However, his boss makes random phone calls to 36 farmers in the sales district and finds that the sales rep only contacted 24 of them in the past year. State the null and alternative hypothesis that the boss should test to determine whether the salesman contacted less than 80% of the farmers in his district in past year.

Ho: p = 0.80 Ha: p < 0.80

A box of Mr. Phipps Tater Crisps is supposed to contain 156 grams of potato chips. On the side of the box it says "This package is sold by weight, not by volume. Packed as full as practicable by modern automatic equipment, it contains full net weight indicated. If it does not appear full when opened, it is because contents have settled during shipping and handling". Periodically, the Nabisco Company receives complaints that their boxes of Tater Crisps are not full (i.e., that they contain less than 156 grams of potato chips). To test this claim, the Nabisco Company randomly samples 10 boxes and finds the average amount of potato chips held by the 10 boxes is 154 grams and the standard deviation is 30 grams. State the null and alternative hypotheses the Nabisco Company wishes to test.

Ho: μ = 156 grams Ha: μ < 156 grams

You are interested in purchasing a new car. One of the many factors you wish to consider is the resale value of the car after 5 yr of ownership. Since you are primarily interested in the Toyota Camry, you decide to estimate the resale value of the Camry with a 90% confidence interval. You manage to obtain data on 17 recently resold 5-yr-old Camrys and derive a 90% confidence interval that is equal to ($10,400, $14,400). How could we alter the sample size and confidence coefficient in order to decrease the width of this confidence interval?

Increase the sample size to 20, but decrease the confidence coefficient to 0.85.

Suppose x has a binomial probability distribution with n = 200 and p = 0.70. We want to determine if it is appropriate to use the normal approximation to the binomial. Which one of the following statements is true?

It is appropriate to use the normal approximation to the binomial, because both 120.558 and 159.442 fall between 0 and n = 200.

A Gallop poll is conducted to estimate the proportion of voters who plan to vote in favor of a certain issuse on the ballet. A random sample of 500 people of voting age is selected. Results of the poll show that 300 of the 500 people polled plan to vote in favor of the issue. Perform the calculations needed to determine whether or not it would be appropriate to construct a large-sample confidence interval for the true population proportion. What do you conclude (i.e., is it appropriate?

It would be appropriate to construct a large-sample confidence interval for the true population proportion, because 0.5343 and 0.6657 both fall between 0 and 1.0.

The amount of money collected by the snack bar at a large university has been recorded daily for the past 5 yr. Records indicate that the mean daily amount collected is $2,500 and the standard deviation is $400. The distribution is skewed to the right due to several high volume days (football Saturdays). Suppose that 100 days were randomly selected from the 5 yr and the average amount of money collected on those days was recorded. Which of the following describes the sampling distribution of the sample mean?

Normally distributed with a mean of $2,500 and a standard deviation of $40.

A __________ __________ of a parameter is a statistic, a single value computed from the observations in a sample, that is used to estimate the value of the target parameter. NOTE: I am looking for the general term, not a specific example.

Point estimate

What assumption is required for estimating the population mean (μ) when we have small samples of n < 30?

The population consisting of all of the values is approximately normally distributed.

The Central Limit Theorem says that the sampling distribution of the sample mean is approximately normal under certain conditions. Which of the following is a necessary condition for the Central Limit Theorem to be used?

The sample size must be large (at least 30 observations).

The Central Limit Theorem says that the sampling distribution of the sample mean is approximately normally distributed under certain conditions. Which of the following is a necessary condition for the Central Limit Theorem to be used?

The sample size must be large (i.e., n must be greater than or equal to 30).

Which of the following statements about the sampling distribution of the sample mean is incorrect?

The standard deviation of the sampling distribution is equal to the population standard deviation, σ.

Which one of the following statements about the sampling distribution of the sample mean is incorrect?

The standard deviation of the sampling distribution is equal to the population standard deviation.

The normal approximation to a binomial probability distribution is reasonably good even for small sample sizes (say, n as small as 10) when p = 0.5 and the distribution of X is therefore symmetric about its mean.

True

The normal approximation to a binomial probability distrubtion is reasonably good even for small sample sizes (say, n as small as 10) when p = 0.5 and the distribution of X is therefore symmetric about its mean.

True

The t and z distributions are very similar. Both are symmetric, mound-shaped, and have a mean of zero.

True

The value of a population parameter (e.g., the mean, μ) is a constant; its value does not change; in other words, it does not vary from sample to sample.

True

An insurance company states that their claim office is able to process all death claims for cattle within 5 working days. Recently there have been several complaints that it took longer than 5 days to process a claim. Top management sets up a statistical test with a null hypothesis that the average time for processing a claim is 5 days and an alternative hypothesis that the average time for processing a claim is greater than 5 days. After completing the statistical test, it is concluded that the average exceeds 5 days. However, it is eventually learned that the mean processing time really is 5 days. What type of error occurred in the statistical test?

Type 1 error

A ________ ________ error occurs if we fail to reject a null hypothesis when it is false.

Type II

Assume that a 90% confidence interval for the mean weight of the population consisting of male students attending OSU is (150 lb, 200 lb). What is the meaning of this 90% confidence interval?

We are 90% confident that the population mean weight of all male students at OSU falls in the interval from 150 to 200 lb.

A large labor union wishes to estimate the mean number of hours per month that union members are absent from work. The union samples 475 of its members at random and monitors their working time for 1 month. At the end of the month, the total number of hours absent from work is recorded for each employee. The mean and standard deviation of the sample are 9.6 hours and 3.6 hours, respectively. What is the correct interpretation of a 95% confidence interval that can be used to estimate the mean (μ) of the entire population of number of hours absent from work per month?

We are 95% confident that the true population mean (μ) falls in the interval that we derived.

A Gallop poll is conducted to estimate the proportion of voters who plan to vote in favor of a school levy in a certain school district. A random sample of 400 people of voting age is selected. Results of the poll show that 240 of the 400 people polled plan to vote in favor of the school levy. Construct a 99% confidence interval for the true population proportion of people who plan to vote in favor of the school levy. What is the meaning of this confidence interval?

We are 99% confident that the true population proportion (p) falls within the interval that we derived.

Assuming that the two sample sizes are the same, find the sample sizes needed to estimate the difference in population proportions correct to within 0.03 with a 90% level of confidence. From prior experience we have an estimate of p1 that it is equal to 0.70 and an estimate of p2 that is equal to 0.60.

We need a sample of 1,354 observations from population 1 and a sample of 1,354 observations from population 2

A scientist conducts an experiment to determine if the mean alkalinity level of water specimens from the Olentangy River is greater than 50 milligrams per liter (mpl). She selects a random sample of 100 water specimens from the river and finds a sample mean of 67.8 mpl and a sample standard deviation of 14.4 mpl. She decides to test the hypothesis using a significance level of 0.01. Using this information concerning the alkalinity level of water from the Olentangy River, which one of the following statements is correct?

We reject the null hypothesis that the population mean equals 50 mpl, because the calculated value of z = 12.36 is greater than the critical value of z = 2.33 at α = 0.01.

Assume that a population of rabbit weights has a uniform distribution, instead of a normal distribution. We calculate the mean of 1,000 random samples from this population, where the number of observations in each sample is equal to 50. Would you expect the 1,000 sample means to be normally distributed?

Yes

Assume that we are interested in the population consisting of the lactation records of all Holstein cows in the U.S. The milk production records have a normal distribution. We select a large number of random samples of size n = 100 from this population and then plot the sample means. Would the sample means still have a normal distribution if the population of milk production records was not normally distributed (e.g., if the population had an exponential distribution)?

Yes

A population of turkeys has a mean weight of 20 lb and a standard deviation of the weights equal to 4 lb. A turkey breeder selects a large number of samples of 36 turkeys each, calculates the mean weight of the turkeys in each of these samples, and then graphs the sample means. Regardless of the shape of the distribution of the population of turkey weights, would we expect the sample means to be approximately normally distributed?

Yes, according to the Central Limit Theorem

We want to test the hypothesis that the mean number of credit hours taken per semester by OSU undergraduates is less than 16 hours. Therefore, we obtain a random sample of credit hours for 49 students. The sample mean is 15 hours and the sample standard deviation is 4 hours. We want to test: Ho: μ = 16 hours Ha: μ < 16 hours using a significance level (α) = 0.01. What is the calculated value of the test statistic needed to test the null hypothesis in this problem?

Z = -1.75

The Kimberly Clark Corporation wants to determine how many tissues a box of Kleenex should contain. Researchers determine that 60 is the average number of tissues used by a typical person during a cold. Suppose a random sample of 100 Kleenex users yielded a sample mean of 56 tissues and a sample standard deviation of 10 tissues used during a typical cold. Kimberly Clark wants to test: Ho: μ = 60 tissues Ha: μ < 60 tissues using a significance level (α) = 0.05. What is the correct value of the test statistic that should be used to test the null hypothesis?

Z = -4.0

Which one of the following confidence intervals would be the widest?

a 99% confidence interval

A standard normal distribution has

a mean of 0 and a standard deviation of 1.

A ______________ of n experimental units is one selected in such a way that every different sample of size n has an equal probability of being selected.

random sample

In seeking a free agent NFL running back, a general manager is looking for a player with a high mean for yards gained per carry and a small standard deviation. Suppose the GM wishes to compare the mean yards gained per carry for two free agents based on independent random samples of their yards gained per carry. Data from last year's pro football season indicate that σ1 and σ2 are both equal to approximately 5 yards. If the GM wants to estimate the difference in means for yards gained per carry by the two running backs correct to within 1 yard with a confidence level of 0.90, how many carries would have to be observed for each of the two players? Assume equal sample sizes.

n1 = n2 = 136 carries for each of the two running backs

Assuming that n1 = n2, find the sample sizes needed to estimate (μ1 - μ2) correct to within 2.5 with probability 0.90. From prior experience we know that σ1 = 18 and σ2 = 16.

n1 = n2 = 252

The FDA wants to compare the mean caffeine contents of two brands of cola, Brand A and Brand B. In a preliminary study, a small number of independent random samples of cans of each brand were selected and the caffeine content of each can was determined. The results were as follows: Brand A Brand B Sample size 15 10 Mean (ounces) 18 20 Variance 1.2 1.5 How many cans of each brand of cola would need to be sampled in order to estimate the difference in poppulation mean caffeine contents to within 0.5 ounces with probability 0.95?

n1 = n2 = 42 cans

We want to use a confidence interval to estimate the proportion of students in the College of Food, Agricultural, and Environmental Sciences that are female. What sample size would be necessary if we want to estimate the true population proportion of female students correct to within 0.03 with probability 0.95? In an earlier small-scale pilot study we obtained an estimate of the proportion of female students (p) that was equal to 0.48.

n= 1,066 students

The College of Food, Agricultural, and Environmental Sciences wants to estimate the proportion of students that are female. In a small pilot study, they obtain a sample estimate of 0.60 for the proportion of students in the college that are female. What sample size would be needed if the college administration wanted to estimate the proportion of students that are female correct to within 0.03 with a probability of 0.98?

n= 1,448

An animal scientist wants to estimate the proportion of heifers that require assistance when giving birth to their first calves. Based on previous research, the animal scientist believes that the proportion of heifers that require assistance is 0.20. How large of a sample does the animal scientist need in order to obtain an estimate of p that is correct to within 0.05 with probability equal to 0.90?

n= 174 heifers

Find the sample size needed to estimate the population proportion (p) correct to within 0.06 with probability 0.95. Assume that we have previous information that indicates that p = 0.30.

n= 225

The Animal Sciences Department wants to estimate the average length of time it takes students to complete a class project correct to within 5 hours with probability 0.98. Determine the sample size needed to estimate the average length of time required to complete the project to within 5 hours with a 98% level of confidence if the standard deviation of the times is 6 hours.

n=8

Suppose that we want to make an inference about the population proportion (p). For sufficiently large sample sizes, the sampling distribution of p-hat is approximately normally distributed with mean equal to __________.

p

Assume that we have 60 plots of ground and that we want to select a random sample of 6 plots for an experiment. We use row 8 of a random number table and go from left to right across the row of random numbers: 96301 91977 05463 07972 18876 20922 94595 56869 69014 60045 18425 84903 42508 32307 Which 6 plots do we include in our random sample?

plots number: 05 07 18 20 56 60

The average litter size in Ohio is approximately 8 pigs per litter. Owners of a particular breed would like to prove that the mean litter size of their breed is greater than 8 pigs per litter. Therefore, they want to test: Ho: μ = 8 pigs/litter Ha: μ > 8 pigs/litter They obtain a random sample of 100 litter size records from sows of this breed and find a sample mean of 8.4 pigs per litter and a sample standard deviation of 1 pig per litter. They decide to use a significance level of α = 0.01. What is the appropriate test statistic needed to test the null hypothesis?

z= 4.0