Question 1

A P-value indicates

Accepted Answer

The P-value is defined as the probability of obtaining a test statistic as extreme as the observed one, assuming that the null hypothesis is true. Therefore, it measures the evidence against the null hypothesis based on the observed data. It does not speak to the probability of the null hypothesis being true or the probability of the alternative hypothesis being true.

Question 2

We have calculated a 95% confidence interval and would like our next confidence interval to have a smaller margin of error without losing any confidence. In order to do this, we can
I. change the z* value to a smaller number
II. take a larger sample
III. take a smaller sample

Accepted Answer

Taking a larger sample size reduces the margin of error while maintaining the same level of confidence.

Question 3

Use the following to answer the question(s) below.
Insurance company records indicate that 10% of its policyholders file claims involving theft or robbery of personal property from their homes. Suppose a random sample of 400 policyholders is selected.
-The probability that the sample proportion of policyholders filing claims involving theft or robbery from their homes is less than 8% is

Accepted Answer

The probability that the sample proportion of policyholders filing claims involving theft or robbery from their homes is less than 8% is 0.0918. This is because the probability of a policyholder filing a claim involving theft or robbery from their home is 10%, and the probability of a sample proportion being less than 8% is 0.0918.

Question 4

Use the following to answer the question(s) below.
Insurance company records indicate that 10% of its policyholders file claims involving theft or robbery of personal property from their homes. Suppose a random sample of 400 policyholders is selected.
-The standard deviation of the sampling distribution of the sample proportion of policyholders filing claims involving theft or robbery from their homes is

Accepted Answer

The standard deviation of the sampling distribution of the sample proportion is calculated using the formula: sqrt[(p(1-p))/n], where p is the population proportion (0.10) and n is the sample size (400). This results in sqrt[(0.10 * 0.90) / 400] = 0.015.

Question 5

Use the following to answer the question(s) below.
In economic downturns companies attempt to downsize their workforces by offering early retirement incentives to older employees. A survey of 723 companies found that 195 engage in such downsizing practices.
-The estimated proportion of companies that downsize their workforces by offering early retirement incentives is

Accepted Answer

The estimated proportion of companies that downsize their workforces by offering early retirement incentives is 195/723 = 0.27, which corresponds to choice D.

Question 6

Use the following to answer the question(s) below.
A men's clothing store has determined the following probability distribution for the number of special size orders placed per month. The distribution is as follows:
Number Ordered Probability
0 0.10
5 0.10
10 0.12
15 0.30
20 0.38
-The number of special size orders this men's clothing store can expect per month is

Accepted Answer

To find the expected number of special size orders per month, multiply each number of orders by its corresponding probability and sum the results: $0(0.10) + 5(0.10) + 10(0.12) + 15(0.30) + 20(0.38) = 0 + 0.5 + 1.2 + 4.5 + 7.6 = 13.8$.

Question 7

Use the following to answer the question(s) below.
The weights of soy patties sold by Veggie Burgers Delight are normally distributed. A random sample of 15 patties yields a mean weight of 108 grams with a sample standard deviation of 14 grams. At the 0.05 level of significance, perform a hypothesis test to see if the true mean weight is less than 113 grams.
-The correct null and alternative hypotheses are

Accepted Answer

Since the question is asking whether the true mean weight is less than 113 grams, the null hypothesis should be that the true mean weight is equal to 113 grams. The alternative hypothesis should be that the true mean weight is less than 113 grams. Thus, the correct null and alternative hypotheses are H0: µ = 113 and HA: µ < 113, which is represented by choice B.

Question 8

Use the following to answer the question(s) below.
The weights of soy patties sold by Veggie Burgers Delight are normally distributed. A random sample of 15 patties yields a mean weight of 108 grams with a sample standard deviation of 14 grams. At the 0.05 level of significance, perform a hypothesis test to see if the true mean weight is less than 113 grams.
-The correct calculated value of the test statistic is

Accepted Answer

The test statistic can be calculated as: 
t = (x̄ - μ)/(s/√n) 
where x̄ is the sample mean, μ is the hypothesized population mean (113 grams in this case), s is the sample standard deviation, and n is the sample size.

Substituting the given values: 
t = (108 - 113)/(14/√15) 
t = -1.38

Looking up the t-distribution table with 14 degrees of freedom (df = n - 1 = 15 - 1), at the 0.05 level of significance and for a left-tailed test (since the alternative hypothesis is less than), the critical value is -1.761.

Since the calculated value of t (-1.38) is greater than the critical value (-1.761), we fail to reject the null hypothesis. Therefore, there is not enough evidence to conclude that the true mean weight is less than 113 grams.

Question 9

A quality assurance manager is interested in determining the likelihood that more than 20 calls come in to a particular customer service centre per hour. What method would be most appropriate for assigning this probability?

Accepted Answer

The most appropriate method for assigning the probability of more than 20 calls coming in per hour would be the relative frequency method, which involves analyzing past data to determine the frequency of occurrence of the event of interest. This method would provide a more objective and empirical estimate of the probability compared to personal, judgmental or subjective methods, which may rely on personal biases or perceptions. The classical method may not be appropriate as it assumes that events are equally likely and independent, which may not be the case in this scenario.

Question 10

Use the following to answer the question(s) below.
A survey of investors finds that 60% use a full service brokerage firm to invest in stocks, 30% trade stocks online and 24% do both.
-What is the probability that an investor selected at random neither uses a full service brokerage firm to invest in stocks nor trades online is

Accepted Answer

The probability that an investor neither uses a full service brokerage firm nor trades online is calculated using the formula for the union of two events: P(A ∪ B) = P(A) + P(B) - P(A ∩ B). Here, P(A) = 60%, P(B) = 30%, and P(A ∩ B) = 24%. So, P(A ∪ B) = 60% + 30% - 24% = 66%. Therefore, the probability that an investor does neither is 1 - 66% = 34%.

Question 11

Use the following to answer the question(s) below.
An advocacy group is investigating whether gender has an effect on job category in large investment firms. She surveyed a sample of firms with the following results:
 
-What is the probability that a randomly selected employee's job category is executive/managerial, given that she is female?

Accepted Answer

The answer of Use the following to answer the question(s)...

Question 12

Use the following to answer the question(s) below.
In economic downturns companies attempt to downsize their workforces by offering early retirement incentives to older employees. A survey of 723 companies found that 195 engage in such downsizing practices.
-The 99% confidence interval for the proportion of companies that downsize their workforces by offering early retirement incentives is

Accepted Answer

The answer of Use the following to answer the question(s)...

Question 13

A truck company wants on-time delivery for 98% of the parts they order from a metal manufacturing plant. They have been ordering from Hudson Manufacturing but will switch to a new, cheaper manufacturer (Steel-R-Us) unless there is evidence that this new manufacturer cannot meet the 98% on-time goal. As a test the truck company purchases a random sample of metal parts from Steel-R-Us, and then determines if these parts were delivered on-time. Which hypotheses should they test?

Accepted Answer

The truck company wants on-time delivery for 98% of the parts they order from a metal manufacturing plant. Hence, the null hypothesis (H0) should be that the proportion of on-time delivery is equal to 0.98 (p=0.98), and the alternative hypothesis (HA) should be that the proportion of on-time delivery is less than 0.98 (p<0.98), as the truck company would switch to a new, cheaper manufacturer only if there is evidence that the new manufacturer cannot meet the 98% on-time goal. Therefore, the correct choice is C: H0: p = 0.98 HA: p < 0.98.

Question 14

Use the following to answer the question(s) below.
A survey of investors finds that 60% use a full service brokerage firm to invest in stocks, 30% trade stocks online and 24% do both.
-The probability that an investor selected at random uses a full service brokerage firm to invest in stocks or trades stocks online is

Accepted Answer

The answer of Use the following to answer the question(s)...

Question 15

Use the following to answer the question(s) below.
A men's clothing store has determined the following probability distribution for the number of special size orders placed per month. The distribution is as follows:
Number Ordered Probability
0 0.10
5 0.10
10 0.12
15 0.30
20 0.38
-The standard deviation in the number of special size orders placed per month is

Accepted Answer

To find the standard deviation, we need to first find the mean (expected value) of the distribution:

Mean = (0)(0.10) + (5)(0.10) + (10)(0.12) + (15)(0.30) + (20)(0.38) 
= 2 + 1.2 + 4.5 + 7.6 
= 15.3

Using the formula for variance, we have:

Variance = [(0 - 15.3)^2(0.10) + (5 - 15.3)^2(0.10) + (10 - 15.3)^2(0.12) + (15 - 15.3)^2(0.30) + (20 - 15.3)^2(0.38)] 
= 73.674

Therefore, the standard deviation is the square root of the variance:

Standard deviation = sqrt(73.674) ≈ 6.60

So, the best choice is D.

Question 16

A theorem that allows us to use the normal probability distribution to approximate the sampling distribution of the sample mean whenever the sample size is large (over 30) is the

Accepted Answer

The central limit theorem states that the sampling distribution of the sample mean will approach a normal distribution as the sample size increases, regardless of the shape of the population distribution. This allows us to use the normal probability distribution to approximate the sampling distribution of the sample mean for large sample sizes.

Question 17

Suppose that a manufacturer is testing one of its machines to make sure that the machine is producing more than 97% good parts (H0: p = 0.97 and HA: p > 0.97). The test results in a P-value of 0.102. In reality, the machine is producing 99% good parts. What probably happens as a result of our testing?

Accepted Answer

Given the P-value of 0.102, we fail to reject the null hypothesis (H0: p = 0.97) because the P-value is greater than the common alpha level of 0.05. However, in reality, the machine is producing 99% good parts, which means it is actually performing better than the null hypothesis suggests. Failing to reject H0 when HA is true (the machine produces more than 97% good parts) leads to a Type II error.

Question 18

We have created a 95% confidence interval for µ with the result (10, 15). What conclusion will we make if we test H0: µ = 16 versus HA: µ ≠ 16 at α = 0.05?

Accepted Answer

The value 16 is not within the 95% confidence interval (10, 15), so we reject the null hypothesis H0: µ = 16.

Question 19

Use the following to answer the question(s) below.
An advocacy group is investigating whether gender has an effect on job category in large investment firms. She surveyed a sample of firms with the following results:
 
-Which of the following statements is true about gender and job category?

Accepted Answer

The fact that there are different proportions of males and females in each job category implies that gender and job category are not independent. If they were independent, we would expect to see similar proportions of males and females in each job category.

Question 20

Use the following to answer the question(s) below.
An advocacy group is investigating whether gender has an effect on job category in large investment firms. She surveyed a sample of firms with the following results:
 
-What is the probability that a randomly selected employee's job category is executive/managerial?

Accepted Answer

The answer of Use the following to answer the question(s)...

Quiz 26: Understanding Probability Distributions and Statistical Inference

A P-value indicates

We have calculated a 95% confidence interval and would like our next confidence interval to have a smaller margin of error without losing any confidence. In order to do this, we can I. change the z* value to a smaller number II. take a larger sample III. take a smaller sample

A quality assurance manager is interested in determining the likelihood that more than 20 calls come in to a particular customer service centre per hour. What method would be most appropriate for assigning this probability?

A theorem that allows us to use the normal probability distribution to approximate the sampling distribution of the sample mean whenever the sample size is large (over 30) is the

We have created a 95% confidence interval for µ with the result (10, 15) . What conclusion will we make if we test H0: µ = 16 versus HA: µ ≠ 16 at α = 0.05?

Use the following to answer the question(s) below. An advocacy group is investigating whether gender has an effect on job category in large investment firms. She surveyed a sample of firms with the following results: -Which of the following statements is true about gender and job category?