Question 1

A sample of 16 ATM transactions shows a mean transaction time of 67 seconds with a standard deviation of 12 seconds.State the hypotheses to test whether the mean transaction time exceeds 60 seconds.
A)H0: μ ≤ 60,H1: μ > 60
B)H0: μ ≥ 60,H1: μ < 60
C)H0: μ = 60,H1: μ ≠ 60
D)H0: μ < 60,H1: μ ≥ 60

Accepted Answer

To test whether the mean transaction time exceeds 60 seconds, we need to use a one-tailed hypothesis test with an alternative hypothesis that the mean transaction time is greater than 60 seconds. Therefore, the correct hypothesis set is:
H0: μ ≤ 60
H1: μ > 60
Option A is the only choice that represents these hypotheses. Option B has the wrong direction for the alternative hypothesis. Option C represents a two-tailed test, which is not applicable to this scenario. Option D has the wrong direction for the null hypothesis.

Question 2

A sample of 16 ATM transactions shows a mean transaction time of 67 seconds with a standard deviation of 12 seconds.Find the critical value to test whether the mean transaction time exceeds 60 seconds at α = .01.
A)2.947
B)2.602
C)2.583
D)2.333

Accepted Answer

The answer of A sample of 16 ATM transactions shows...

Question 3

Last year,10 percent of all teenagers in Greenville purchased a new iPhone.This year,a sample of 260 randomly chosen Greenville teenagers showed that 39 had purchased a new iPhone.To test whether the percentage has risen,the critical value at α = .05 is
A)1.645
B)1.658
C)1.697
D)1.960

Accepted Answer

The critical value for a one-tailed test at α = .05 is 1.645. This is used to determine if the sample proportion significantly exceeds the hypothesized population proportion.

Question 4

A sample of 16 ATM transactions shows a mean transaction time of 67 seconds with a standard deviation of 12 seconds.Find the test statistic to decide whether the mean transaction time exceeds 60 seconds.
A)1.457
B)2.037
C)2.333
D)1.848

Accepted Answer

The test statistic 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, $s$ is the sample standard deviation, and $n$ is the sample size. Plugging in the given values: $t = \frac{67 - 60}{(12/\sqrt{16})} = \frac{7}{3} = 2.333$.

Question 5

Given that in a one-tailed test you cannot reject H0,can you reject H0 in a two-tailed test at the same α?
A)Yes.
B)No.
C)Maybe.

Accepted Answer

In a two-tailed test, the rejection region is split into two tails, so the critical value for rejection is spread across both tails. Therefore, the critical value is more stringent in a two-tailed test than in a one-tailed test, making it harder to reject the null hypothesis. Since you cannot reject H0 in a one-tailed test, you cannot reject H0 in a two-tailed test at the same alpha level (assuming the same sample size and standard deviation).

Question 6

At α = .05,the critical value to test the hypotheses H0: π ≥ .40,H1: π < .40 would be
A)−1.645
B)−1.960
C)−2.326
D)impossible to determine without more information.

Accepted Answer

The critical value for a one-tailed test at α = 0.05 is -1.645 when testing if π < .40.

Question 7

The process that produces Sonora Bars (a type of candy)is intended to produce bars with a mean weight of 56 gm.The process standard deviation is known to be 0.77 gm.A random sample of 49 candy bars yields a mean weight of 55.82 gm.Find the test statistic to see whether the candy bars are smaller than they are supposed to be.
A)−1.636
B)−1.645
C)−1.677

Accepted Answer

The answer of The process that produces Sonora Bars (a...

Question 8

Which of the following decisions could result in a Type II error for a test?
A)Reject the alternative hypothesis.
B)Reject the null hypothesis.
C)Fail to reject the null hypothesis.
D)Make no decision.

Accepted Answer

A Type II error occurs when the null hypothesis is true but we fail to reject it. Therefore, failing to reject the null hypothesis (choice C) could result in a Type II error.

Question 9

The hypotheses H0: π ≥ .40,H1: π < .40 would require
A)a left-tailed test.
B)a right-tailed test.
C)a two-tailed test.

Accepted Answer

The null hypothesis states that the population proportion is greater than or equal to 0.40 (π ≥ 0.40), while the alternative hypothesis states that the population proportion is less than 0.40 (π < 0.40). This indicates a one-tailed or directional hypothesis, where we are interested in testing if the proportion is significantly smaller than a specified value. Since H1 represents a smaller proportion value, we need to conduct a left-tailed test to determine if there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis. Therefore, the best choice is A, a left-tailed test.

Question 10

The process that produces Sonora Bars (a type of candy)is intended to produce bars with a mean weight of 56 gm.The process standard deviation is known to be 0.77 gm.A random sample of 49 candy bars yields a mean weight of 55.82 gm.Find the p-value for a test to see whether the candy bars are smaller than they are supposed to be.
A)Between .05 and .10
B)Between .025 and .05
C)Between .01 and .025
D)Less than .01

Accepted Answer

To find the p-value for a one-tailed test (since we're testing if the candy bars are smaller than they are supposed to be), we first calculate the z-score using the formula $z = \frac{\bar{x} - \mu}{(\sigma/\sqrt{n})}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values, we get $z = \frac{55.82 - 56}{(0.77/\sqrt{49})} = \frac{-0.18}{0.11} = -1.636$. Looking up the z-score of -1.636 in a standard normal distribution table or using a calculator, we find that the p-value is between .05 and .10, indicating the probability of observing a sample mean of 55.82 gm or less by chance if the true mean is 56 gm.

Question 11

Last year,10 percent of all teenagers in Greenville purchased a new iPhone.This year,a sample of 260 randomly chosen Greenville teenagers showed that 39 had purchased a new iPhone.To test whether the percentage has risen,the p-value is approximately
A).0501
B).0314
C).0492
D).0036

Accepted Answer

The p-value is the probability of getting a sample result as extreme as or more extreme than the one observed, assuming the null hypothesis is true. In this case, the null hypothesis is that the percentage of teenagers who purchased a new iPhone has not changed from last year, which is 10%. The sample result is that 39 out of 260 teenagers purchased a new iPhone, which is a proportion of 39/260 = 0.15. To calculate the p-value, we can use a binomial distribution with n = 260 and p = 0.10. The p-value is the probability of getting a proportion of 0.15 or more extreme, which is approximately 0.0036.

Question 12

In a test of a mean,the reported p-value is .025.Using α = .05 the conclusion would be to
A)accept the null hypothesis.
B)reject the null hypothesis.
C)fail to reject the null hypothesis.
D)gather more evidence due to inconclusive results.

Accepted Answer

The p-value of .025 is less than the significance level of .05, indicating that the results are statistically significant. Therefore, we reject the null hypothesis.

Question 13

In the nation of Gondor,the EPA requires that half the new cars sold will meet a certain particulate emission standard a year later.A sample of 64 one-year-old cars revealed that only 24 met the particulate emission standard.The test statistic to see whether the proportion is below the requirement is
A)−1.645
B)−2.066
C)−2.000
D)−1.960

Accepted Answer

The test statistic is calculated using the formula for a proportion test: $z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$, where $\hat{p}$ is the sample proportion, $p_0$ is the hypothesized population proportion, and $n$ is the sample size. Here, $\hat{p} = \frac{24}{64} = 0.375$, $p_0 = 0.5$, and $n = 64$. Plugging these values into the formula gives $z = \frac{0.375 - 0.5}{\sqrt{\frac{0.5(0.5)}{64}}} = -2.000$.

Question 14

The process that produces Sonora Bars (a type of candy)is intended to produce bars with a mean weight of 56 gm.The process standard deviation is known to be 0.77 gm.A random sample of 49 candy bars yields a mean weight of 55.82 gm.Which are the hypotheses to test whether the mean is smaller than it is supposed to be?
A)H0: μ ≤ 56,H1: μ > 56
B)H0: μ ≥ 56,H1: μ < 56
C)H0: μ = 56,H1: μ ≠ 56
D)H0: μ < 56,H1: μ ≥ 56

Accepted Answer

Since the question is asking if the mean weight is smaller than it is supposed to be (which is 56 gm), the alternative hypothesis should state that the population mean is less than 56 gm. Therefore, the correct hypothesis statements are: H0: μ ≥ 56, H1: μ < 56. The option (B) is the only one that matches this criterion.

Question 15

For a right-tailed test of a hypothesis for a single population mean with n = 10,the value of the test statistic was t = 1.411.The p-value is
A)between .05 and .025.
B)between .10 and .05.
C)greater than .10.
D)less than .001.

Accepted Answer

For a right-tailed test with a t-value of 1.411 and 9 degrees of freedom (n-1 = 10-1 = 9), the p-value can be found using a t-table or a calculator. Using a t-table, we find the area to the right of 1.411 for 9 degrees of freedom is between .10 and .05. Therefore, the p-value is between .10 and .05, which corresponds to choice B.

Question 16

Last year,10 percent of all teenagers in Greenville purchased a new iPhone.This year,a sample of 260 randomly chosen Greenville teenagers showed that 39 had purchased a new iPhone.The test statistic to find out whether the percentage has risen would be
A)2.687
B)2.758
C).0256
D)2.258

Accepted Answer

The test statistic is calculated using the formula for a proportion: (p̂ - p0) / √(p0(1-p0)/n), where p̂ is the sample proportion (39/260), p0 is the population proportion (0.10), and n is the sample size (260). This calculation results in approximately 2.687.

Question 17

Ajax Peanut Butter's quality control allows 2 percent of the jars to exceed the quality standard for insect fragments.A sample of 150 jars from the current day's production reveals that 30 exceed the quality standard for insect fragments.Which is incorrect?
A)Normality of p may safely be assumed in the hypothesis test.
B)A right-tailed test would be appropriate.
C)We strongly suspect that quality control standards are not met.
D)Type II error is more of a concern in this case than Type I error.

Accepted Answer

The answer of Ajax Peanut Butter's quality control allows 2...

Question 18

The Melodic Kortholt Company will change its current health plan if at least half the employees are dissatisfied with it.A trial sample of 25 employees shows that 16 are dissatisfied.The p-value for a right-tailed test is
A).1337
B).4192
C).0901
D).0808

Accepted Answer

The p-value of .0808 suggests that there is an 8.08% chance of observing a sample with 16 or more dissatisfied employees out of 25 if the true proportion of dissatisfied employees in the company does not exceed half. This relatively low p-value indicates evidence against the null hypothesis (that half or fewer are dissatisfied), supporting the consideration for changing the health plan.

Question 19

The Melodic Kortholt Company will change its current health plan if at least half the employees are dissatisfied with it.A trial sample of 25 employees shows that 16 are dissatisfied.In this problem
A)normality of the sample proportion should not be assumed.
B)normality of the sample proportion can be assumed.
C)normality of the sample proportion cannot be judged without knowing π.

Accepted Answer

According to the Central Limit Theorem, for a sample size of n >= 30, the sample proportion will be approximately normally distributed, regardless of the true proportion. In this case, we have a sample size of 25, which is slightly below 30, but still considered large enough to assume normality of the sample proportion. Therefore, choice B is the best choice.

Question 20

Given H0: μ ≥ 18 and H1: μ < 18,we would commit a Type I error if we
A)conclude that μ ≥ 18 when the truth is that μ < 18.
B)conclude that μ < 18 when the truth is that μ ≥ 18.
C)fail to reject μ ≥ 18 when the truth is that μ < 18.

Accepted Answer

A Type I error occurs when we reject the null hypothesis (H0: μ ≥ 18) when it is actually true. In this case, the null hypothesis states that the population mean is greater than or equal to 18. Therefore, we would commit a Type I error if we incorrectly conclude that the population mean is less than 18 (i.e. H1: μ < 18) when it is actually greater than or equal to 18. This corresponds to choice B.

Quiz 9: One-Sample Hypothesis Tests

A sample of 16 ATM transactions shows a mean transaction time of 67 seconds with a standard deviation of 12 seconds.State the hypotheses to test whether the mean transaction time exceeds 60 seconds.

A sample of 16 ATM transactions shows a mean transaction time of 67 seconds with a standard deviation of 12 seconds.Find the critical value to test whether the mean transaction time exceeds 60 seconds at α = .01.

Last year,10 percent of all teenagers in Greenville purchased a new iPhone.This year,a sample of 260 randomly chosen Greenville teenagers showed that 39 had purchased a new iPhone.To test whether the percentage has risen,the critical value at α = .05 is

A sample of 16 ATM transactions shows a mean transaction time of 67 seconds with a standard deviation of 12 seconds.Find the test statistic to decide whether the mean transaction time exceeds 60 seconds.

Given that in a one-tailed test you cannot reject H0,can you reject H0 in a two-tailed test at the same α?

At α = .05,the critical value to test the hypotheses H0: π ≥ .40,H1: π < .40 would be

Which of the following decisions could result in a Type II error for a test?

The hypotheses H0: π ≥ .40,H1: π < .40 would require

Last year,10 percent of all teenagers in Greenville purchased a new iPhone.This year,a sample of 260 randomly chosen Greenville teenagers showed that 39 had purchased a new iPhone.To test whether the percentage has risen,the p-value is approximately

In a test of a mean,the reported p-value is .025.Using α = .05 the conclusion would be to

For a right-tailed test of a hypothesis for a single population mean with n = 10,the value of the test statistic was t = 1.411.The p-value is

Last year,10 percent of all teenagers in Greenville purchased a new iPhone.This year,a sample of 260 randomly chosen Greenville teenagers showed that 39 had purchased a new iPhone.The test statistic to find out whether the percentage has risen would be

Ajax Peanut Butter's quality control allows 2 percent of the jars to exceed the quality standard for insect fragments.A sample of 150 jars from the current day's production reveals that 30 exceed the quality standard for insect fragments.Which is incorrect?

The Melodic Kortholt Company will change its current health plan if at least half the employees are dissatisfied with it.A trial sample of 25 employees shows that 16 are dissatisfied.The p-value for a right-tailed test is

The Melodic Kortholt Company will change its current health plan if at least half the employees are dissatisfied with it.A trial sample of 25 employees shows that 16 are dissatisfied.In this problem

Given H0: μ ≥ 18 and H1: μ < 18,we would commit a Type I error if we