10. the true population average commute distance. 11. Suppose you interview 10 r

Question

10.

the true population average commute distance.

11.

Suppose you interview 10 randomly selected workers and ask how many miles they commute to work. You'll compute the sample mean commute distance. Now imagine repeating the survey many, many times, each time recording a different sample mean commute distance. In the long run, a histogram of these sample means represents: the bias, if any, that is present in the sampling method. a simple random sample. the sampling distribution of the sample mean.

the true population average commute distance.

11.

Suppose that two very large companies (A and B) each select random samples of their employees. Company A has 5000 employees and Company B has 15,000 employees. In both surveys, the company will record the number of sick days taken by each sampled employee. If each company randomly selects 50 employees for the survey, which statement is TRUE about the sampling distributions of the sample means (the mean number of sick days)? None of the above Since Company A is surveying a higher percent of its employees, the standard deviation of the sampling distribution for its sample mean will be smaller than that for Company B (the larger company). Larger companies should take larger samples. Since Company B is a larger company, the standard deviation for its sampling distribution of the sample mean is smaller. The larger a population, the smaller the standard deviation of a sample mean's sampling distribution. The sampling distributions of the sample means will have about the same standard deviation. The standard deviation for a sampling distribution of a sample mean depends only on the sample size, not the population (company) size. 12. Suppose that two very large companies (A and B) each select random samples of their employees. Company A has 5000 employees and Company B has 15,000 employees. In both surveys, the company will record the number of sick days taken by each sampled employee. If each firm randomly selects 3% of its employees, which statement is TRUE about the sampling distributions of the sample means? None of the above The standard deviation of the sampling distribution of the sample mean will be smaller for the larger company (Company B) because a larger sample is being selected. The sampling distributions of the sample means will have about the same standard deviation because in both cases we're selecting 3% of the employees. The smaller company (Company A) will have a sampling distribution with smaller standard deviation. 13. The incomes in a certain large population of college teachers have a Normal distribution with mean $75,000 and standard deviation $10,000. Sixteen teachers are selected at random from this population to serve on a committee. What is the probability that their average salary is more than $77,500? 0.8413 0.1587 essentially 0 0.0228 14. The distribution of actual weights of 8-ounce wedges of cheddar cheese produced at a dairy is Normal with mean 8.1 ounces and standard deviation 0.2 ounces. A sample of 10 of these cheese wedges is selected. The distribution of the sample mean of the weights of cheese wedges is: approximately Normal, mean 8.1, standard deviation 0.2. approximately Normal, mean 8.1, standard deviation 0.020. It is not possible to tell because the sample size is too small. approximately Normal, mean 8.1, standard deviation 0.063. 15. The distribution of actual weights of 8-ounce wedges of cheddar cheese produced at a dairy is Normal with mean 8.1 ounces and standard deviation 0.2 ounces. A sample of 10 of these cheese wedges is selected. What is the standard deviation of the sampling distribution of the mean? 0.075 ounces 0.963 ounces 0.315 ounces 0.0633 ounces 16. The distribution of actual weights of 8-ounce wedges of cheddar cheese produced at a dairy is Normal with mean 8.1 ounces and standard deviation 0.2 ounces. A sample of 10 of these cheese wedges is selected. The company decides instead to sample batches of 20 cheese wedges, and the sampling is repeated every time workers start a new shift at the dairy. How will the distribution of the sample means of the weights of cheese wedges change from the previous batches, which only contained 10 samples? The distribution will still be Normal, but it will be more peaked around the sample mean and the standard deviation will be larger. The distribution will still be Normal, but it will be more peaked around the sample mean and the standard deviation will be smaller. The shape of the distribution may change completely based on the new data. It is not possible to tell from the information provided. 17. The variability of a statistic is described by the: stability of the population it describes. amount of bias present. spread of its sampling distribution. vagueness in the wording of the question used to collect the sample data. 18. Incomes in a certain town are strongly right skewed with mean $36,000 and standard deviation $7000. A random sample of 10 households is taken. What is the probability the average of the sample is more than $38,000? Cannot say. 0.1831. 0.3875. 19. Which sample size will give me the smallest standard deviation of x? 36. Both will be the same. 35. 20. I took a large sample of households in a city, and based on that, estimate the standard deviation of the income for all households in the city is $800. In order to make a desired conclusion about the income for all the households in the city, I want the sample mean for another sample to have a standard deviation of no more than $100. How many households must I have in this new sample? 64. 100. 8.

Explanation / Answer

Question 10

Answer:

The sampling distribution of the sample mean

Explanation:

We know that the distribution of any sample statistic represent the sampling distribution for this sample statistic. For this scenario, the sampling distribution of the sample means is consider for drawing the histogram.

Question 11

Answer:

Since Company B is a larger company, the standard deviation for its sampling distribution of the sample mean is smaller. The larger a population, the smaller the standard deviation of a sample mean's sampling distribution.

Explanation:

We know that the estimate for the standard deviation for the sampling distribution of the sample mean is given as the population standard deviation divided by the square root of sample size n. When we increase the sample size n, the standard deviation will be decrease. So, for the larger population size, the standard deviation of sampling distribution of mean (or standard error) would be smaller.

Question 12

Answer:

The sampling distributions of the sample means will have about the same standard deviation because in both cases we're selecting 3% of the employees.

Explanation:

For the given two sampling distributions, about 3% of employees are selected. This means equal proportions of employees are selected for both companies. For the sampling distribution with long run, the standard deviations will be approximately same.

Question 13

Answer:

We are given incomes follows normal distribution with mean = µ = 75000 and SD = = 10000

We are given sample size = n = 16

We have to find P(Xbar > 77500)

P(Xbar > 77500) = 1 – P(Xbar < 77500)

The Z-score formula is given as below:

Z = (Xbar - µ) / [ / n]

Z = (77500 – 75000) / [10000 / sqrt(16)]

Z = 2500/2500 = 1

P(Xbar < 77500) = P(Z<1) = 0.841345

P(Xbar > 77500) = 1 – P(Xbar < 77500)

P(Xbar > 77500) = 1 – 0.841345

P(Xbar > 77500) = 0.158655

Required Probability = 0.1587

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