Question 1

11eb4928_20e5_2653_b114_89e4aed1891b_TB7192_00

Accepted Answer

The test statistic for a one-sample t-test is calculated using the formula $t = \frac{\bar{x} - \mu}{(s/\sqrt{n})}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean under the null hypothesis, $s$ is the sample standard deviation, and $n$ is the sample size. Plugging in the given values ($\bar{x} = 16.6$, $\mu = 15$, $s = 2.22$, $n = 24$), the calculation yields $t = 3.532$, indicating that the sample mean is significantly higher than the hypothesized mean, assuming the null hypothesis that the mean is 15 hours per month.

Question 2

A psychologist claims that more than 2.2% of the population suffers from professional problems due to extreme shyness.Identify the Type II in this context.&#10;A)The error of accepting the claim that the true proportion is more than 2.2% when it really is more than 2.2%.&#10;B)The error of rejecting the claim that the true proportion is more than 2.2% when it really is more than 2.2%.&#10;C)The error of rejecting the claim that the true proportion is at most 2.2% when it really is at most 2.2%.&#10;D)The error of failing to reject the claim that the true proportion is at most 2.2% when it is actually more than 2.2%.&#10;E)The error of failing to accept the claim that the true proportion is at most 2.2% when it is actually more than 2.2%.

Accepted Answer

A Type II error occurs when the null hypothesis is not rejected when it is false. In this context, the null hypothesis would likely be that the true proportion is at most 2.2%. Failing to reject this claim when the true proportion is actually more than 2.2% corresponds to a Type II error.

Question 3

Insurance companies track life expectancy information to assist in determining the cost of life insurance policies.Last year the average life expectancy of all policyholders was 77
Years.ABI Insurance wants to determine if their clients now have a longer life expectancy,
On average, so they randomly sample some of their recently paid policies.The insurance
Company will only change their premium structure if there is evidence that people who buy
Their policies are living longer than before.Which of the following statement is true about
This hypothesis test?

A)It is a one tailed test about a mean.
B)It is a one tailed test about a proportion.
C)It is a two tailed test about a mean.
D)It is a two tailed test about a proportion.

A

Accepted Answer

The hypothesis test is focused on determining if the life expectancy has increased, which is a specific direction (longer life expectancy), making it a one-tailed test. Since life expectancy is a numerical value (years), it concerns a mean rather than a proportion.

Question 4

11eb4928_20e5_4d65_b114_b9efc3a2c37a_TB7192_00

Accepted Answer

A Type I error occurs when the null hypothesis ($H_0$) is rejected when it is actually true. In this scenario, rejecting $H_0$ means incorrectly concluding that the mean battery life has increased (is greater than $8.3$ hours) when in reality, it has not changed and remains at $8.3$ hours.

Question 5

A company that sells eco-friendly cleaning products is concerned that only 19.5% of people who use such products select their brand.A marketing director suggests that the company
Invest in new advertising and labeling to strengthen its green image.The company decides to
Do so in a test market so that the effectiveness of the marketing campaign may be evaluated.
In this context, committing a Type I error
I)Occurs when they conclude that the percentage of customers purchasing the company's
Brand has increased when in fact it has not.
II)Occurs then they conclude that the percentage of customers purchasing the company's
Brand has not increased when in fact it has.
III)Would result in the company wasting money on a new marketing campaign that does not
Increase the percentage of customers buying their brand.

A)I only
B)II only
C)III only
D)Both I and III

Accepted Answer

A Type I error occurs when a false positive result is concluded, meaning the company believes the new marketing campaign is effective when it is not, leading to unnecessary expenditure (I and III). Type II error, not listed here, would involve failing to detect a true effect (II).

Question 6

11eb4928_20e5_e9ad_b114_23d6ebdea51f_TB7192_00

Accepted Answer

The $P$-value of $0.006$ indicates a statistically significant increase in sales, as it is less than the alpha level of $0.05$, suggesting the increase in spending is not due to random chance.

Question 7

11eb4928_20e5_e9ac_b114_3f9f2a7d7781_TB7192_00

Accepted Answer

A Type II error occurs when the null hypothesis ($H_0$) is not rejected when it is false. In this context, it means the teacher would conclude that the mean math SAT score has not changed from 472, when in reality, it has changed (either increased or decreased).

Question 8

11eb4928_20e4_ff42_b114_7b35997fc803_TB7192_00

Accepted Answer

The answer of 11eb4928_20e4_ff42_b114_7b35997fc803_TB7192_00...

Question 9

11eb4928_20e5_9b89_b114_5108caad000e_TB7192_00

Accepted Answer

The p-value of 0.063 is greater than the significance level $\alpha = 0.05$, which means we do not have enough evidence to reject the null hypothesis. Therefore, we fail to reject the null hypothesis and conclude that there is not significant evidence to indicate an increase in average life expectancy.

Question 10

Top management of a large multinational corporation wants to create a culture of innovativeness and change.A consultant hired to assess the company's organizational culture
Finds that only 15% of employees are open to new ideas and approaches toward their work.
Consequently, the company conducts a program for employees in order to reinforce the new
Corporate philosophy.After the program is completed, employees are surveyed to see if a
Greater percentage is now open to innovativeness and change.The correct alternative
Hypothesis is

Accepted Answer

The correct alternative hypothesis is $p > 0.15$ because the company aims to increase the proportion of employees open to new ideas and approaches, indicating a desire for a percentage greater than 15%.

Question 11

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Accepted Answer

The answer of 11eb4928_20e5_7478_b114_1f7e0ce9ac1d_TB7192_00...

Question 12

11eb4928_20e5_4d66_b114_7ba5a9119497_TB7192_00

Accepted Answer

The answer of 11eb4928_20e5_4d66_b114_7ba5a9119497_TB7192_00...

Question 13

11eb4928_20e5_2654_b114_8528112b34d1_TB7192_00

Accepted Answer

The answer of 11eb4928_20e5_2654_b114_8528112b34d1_TB7192_00...

Question 14

Which of the following would increase the power of a test? I.Increase the sample size
II)Decrease the significance level
III)Increase alpha

A)I only
B)II only
C)III only
D)I and II
E)I and III

Accepted Answer

The answer of Which of the following would increase the...

Question 15

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Accepted Answer

The answer of 11eb4928_20e5_c29b_b114_e1d42efdb65f_TB7192_00...

Question 16

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Accepted Answer

The answer of 11eb4928_20e5_c29a_b114_230437150ffb_TB7192_00...

Question 17

Top management of a large multinational corporation wants to create a culture of innovativeness and change.A consultant hired to assess the company's organizational culture
Finds that only 15% of employees are open to new ideas and approaches toward their work.
Consequently, the company conducts a program for employees in order to reinforce the new
Corporate philosophy.After the program is completed, employees are surveyed to see if a
Greater percentage is now open to innovativeness and change.Suppose that based on the
Sample results the company rejects the null hypothesis when in fact it is true.Which of the
Following statements is correct?

A)This led to the conclusion that the percentage of employees open to new ideas did not increase when in fact it did.
B)This led to the conclusion that the percentage of employees open to new ideas did increase when in fact it did not.
C)This is known as a fatal error.
D)This is known as a Type II error.

Accepted Answer

The answer of Top management of a large multinational corporation...

Deck 19: More About Tests and Intervals