Question 1

Find the critical value and rejection region for the type of z-test with level of significance α $\alpha$ Two-tailed test, α $\alpha = 0.10$ A) $- z _ { 0 } = - 1.645 , z _ { 0 } = 1.645 ; z < - 1.645 , z > 1.645$ B) $- z _ { 0 } = - 2.33 , z _ { 0 } = 2.33 ; z < - 2.33 , z > 2.33$ C) $- \mathrm { z } _ { 0 } = - 2.575 , \mathrm { z } _ { 0 } = 2.575 ; \mathrm { z } < - 2.575 , \mathrm { z } > 2.575$ D) $- z _ { 0 } = - 1.96 , z _ { 0 } = 1.96 ; z < - 1.96 , z > 1.96$

Accepted Answer

For a two-tailed test with $\alpha = 0.10$, the critical values are found by dividing the significance level by 2 for each tail ($0.05$ in each tail). Looking up $0.05$ in the z-table gives a z-score of approximately $1.645$, thus the critical values are $-1.645$ and $1.645$, and the rejection regions are $z < -1.645$ and $z > 1.645$.

Question 2

Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject $\mathrm { H } _ { 0 }$ for the level of significance α $\alpha$ Left-tailed test
Z = -1.83 $\alpha$ α = 0.05
A)0.0336; reject $\mathrm { H } _ { 0 }$
B)0.0672; reject $\mathrm { H } _ { 0 }$
C)0.9664; fail to reject $\mathrm { H } _ { 0 }$
D)0.0672; fail to reject $\mathrm { H } _ { 0 }$

Accepted Answer

For a left-tailed test with $Z = -1.83$, the p-value can be found using a standard normal distribution table or a calculator, which gives approximately 0.0336. Since the p-value (0.0336) is less than the significance level $\alpha = 0.05$, we reject $H_0$.

Question 3

Test the claim about the population mean $\mu$ at the level of significance α. Assume the population is normally distributed. Claim: $\mu > 28 ; \alpha = 0.05 ; \sigma = 1.2$
Sample statistics: $\bar { x } = 28.3 , n = 50$
A)Reject $\mathrm { H } _ { 0 }$ . There is enough evidence at the 5% level of significance to support the claim.
B)Fail to reject $\mathrm { H } _ { 0 } \text {. }$ There is not enough evidence at the 5% level of significance to support the claim.
C)Not enough information to decide.

Accepted Answer

To test the claim, we use the formula for the z-test since $\sigma$ is known: $z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}}$. Plugging in the given values: $z = \frac{28.3 - 28}{1.2/\sqrt{50}}$, we find that z is greater than the critical value for $\alpha = 0.05$ in a right-tailed test. Therefore, we reject $H_0$ and conclude there is enough evidence to support the claim that $\mu > 28$.

Question 4

Given $\mathrm { H } _ { 0 } : \mu \geq 23.5 \text { and } \alpha = 0.05 \text {, }$ which level of confidence should you use to test the claim?
A)90%
B)99%
C)80%
D)95%

Accepted Answer

The answer of Given \(\mathrm { H } _ {...

Question 5

Given $\mathrm { H } _ { 0 } : \mu \leq 12$ for which confidence interval should you reject $\mathrm { H } _ { 0 } ?$
A)(13, 16)
B)(11.5, 12.5)
C)(10, 13)

Accepted Answer

A confidence interval that does not include the null hypothesis value ($\mu \leq 12$) indicates that the null hypothesis can be rejected. Choice A, (13, 16), does not include 12, so it suggests rejecting $\mathrm { H } _ { 0 }$.

Question 6

Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject $\mathrm { H } _ { 0 }$ for the level of significance α $\alpha$ Two-tailed test
Z = 1.95 $\alpha$ = 0.05
A)0.0512; fail to reject $\mathrm { H } _ { 0 }$
B)0.0256; reject $\mathrm { H } _ { 0 }$
C)0.0512; reject $\mathrm { H } _ { 0 }$
D)0.9744; fail to reject $\mathrm { H } _ { 0 }$

Accepted Answer

For a two-tailed test with $Z = 1.95$ and $\alpha = 0.05$, the p-value is found by looking up the Z-score in a standard normal distribution table or using a calculator. The area to the right of $Z = 1.95$ is approximately 0.0256. Since it's a two-tailed test, we double this value to get the p-value, which is approximately 0.0512. Since the p-value (0.0512) is greater than $\alpha$ (0.05), we fail to reject the null hypothesis $\mathrm { H } _ { 0 }$.

Question 7

Find the critical value and rejection region for the type of z-test with level of significance α. Two-tailed test, α $\alpha = 0.01$ A) $- z _ { 0 } = - 2.575 , z _ { 0 } = 2.575 ; z < - 2.575 , z > 2.575$ B) $- z _ { 0 } = - 2.33 , z _ { 0 } = 2.33 ; z < - 2.33 , z > 2.33$ C) $- z _ { 0 } = - 1.645 , z _ { 0 } = 1.645 ; z < - 1.645 , z > 1.645$ D) $- z _ { 0 } = - 1.96 , z _ { 0 } = 1.96 ; z < - 1.96 , z > 1.96$

Accepted Answer

For a two-tailed test with a significance level of $\alpha = 0.01$, the critical values are found by dividing the significance level by 2 (for the two tails) and looking up the corresponding z-value that accumulates the middle 98% of the distribution. The critical z-values are $\pm 2.575$, indicating rejection regions for z-scores less than -2.575 or greater than 2.575.

Question 8

The P-value for a hypothesis test is P = 0.006. Do you reject or fail to reject $\mathrm { H } _ { 0 }$ when the level of significance is $\alpha$ α = 0.01?
A)reject $\mathrm { H } _ { 0 }$
B)fail to reject $\mathrm { H } _ { 0 }$
C)not sufficient information to decide

Accepted Answer

The P-value (0.006) is less than the significance level ($\alpha = 0.01$), so we reject the null hypothesis $\mathrm { H } _ { 0 }$.

Question 9

The P-value for a hypothesis test is P = 0.066. Do you reject or fail to reject $\mathrm { H } _ { 0 }$ when the level of significance is $\alpha$ = 0.05?
A)fail to reject $\mathrm { H } _ { 0 }$
B)reject $\mathrm { H } _ { 0 }$
C)not sufficient information to decide

Accepted Answer

Since the P-value (0.066) is greater than the significance level ($\alpha$ = 0.05), we fail to reject the null hypothesis $\mathrm { H } _ { 0 }$.

Question 10

Given $\mathrm { H } _ { 0 } : \mathrm { p } \geq 0.45 \text {, }$ for which confidence interval should you reject $\mathrm { H } _ { 0 } ?$
A)(0.32, 0.40)
B)(0.40, 0.50)
C)(0.42, 0.47)

Accepted Answer

The confidence interval (0.32, 0.40) does not include the null hypothesis value of $p = 0.45$, indicating that the true proportion is likely less than 0.45, leading to rejection of $H_0$.

Question 11

Find the critical value and rejection region for the type of z-test with level of significance α $\alpha _ { 2 }$ Right-tailed test, α $\alpha$ = 0.01
A) $z _ { 0 } = 2.33 ; z > 2.33$
B) $z _ { 0 } = 2.575 ; z > 2.575$
C) $z _ { 0 } = 1.645 ; z > 1.645$
D) $\mathrm { z } _ { 0 } = 1.96 ; ; \mathrm { z } > 1.96$

Accepted Answer

For a right-tailed test with α = 0.01, the critical value is 2.33, and the rejection region is z > 2.33.

Question 12

Find the critical value and rejection region for the type of z-test with level of significance α $\alpha$ Two-tailed test, α $\alpha$ = 0.06 A)- $- z _ { 0 } = - 1.88 , z _ { 0 } = 1.88 ; z < 1.88 , z > 1.88$ B) $- \mathrm { z } _ { 0 } = - 2.33 , \mathrm { z } _ { 0 } = 2.33 ; \mathrm { z } < - 2.33 , \mathrm { z } > 2.33$ C)- $- z _ { 0 } = - 2.575 , z _ { 0 } = 2.575 ; z < - 2.575 , z > 2.575$ D) $- z _ { 0 } = - 1.96 , z _ { 0 } = 1.96 ; z < - 1.96 , z > 1.96$

Accepted Answer

For a two-tailed test with $\alpha = 0.06$, the significance level is split between the two tails, so each tail has an area of $0.03$. Looking up the z-value for $0.03$ in the z-table (or using a calculator), we find the critical value closest to $0.03$ in the tail is approximately $1.88$. Thus, the rejection regions are $z < -1.88$ and $z > 1.88$.

Question 13

Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject $\mathrm { H } _ { 0 }$ for the level of significance α $\alpha .$ Left-tailed test
Z = -2.05 $\alpha$ = 0.05
The test statistic in a left-tailed test is z = -2.05.
A)0.0202; reject $\mathrm { H } _ { 0 }$
B)0.4798; fail to reject $\mathrm { H } _ { 0 }$
C)0.0404; reject $\mathrm { H } _ { 0 }$
D)0.0453 fail to reject $\mathrm { H } _ { 0 }$

Accepted Answer

The P-value for a z-score of -2.05 in a left-tailed test is approximately 0.0202. Since this P-value is less than the significance level of 0.05, we reject the null hypothesis $\mathrm { H } _ { 0 }$.

Question 14

Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject $\mathrm { H } _ { 0 }$ for the level of significance α $\alpha$ Right-tailed test
Z = 1.43 $\alpha$ = 0.05
A)0.0764; Fail to reject $\mathrm { H } _ { 0 }$
B)0.0764; reject $\mathrm { H } _ { 0 }$
C)0.1528; fail to reject $\mathrm { H } _ { 0 }$
D)0.1528; reject $\mathrm { H } _ { 0 }$

Accepted Answer

For a right-tailed test with $Z = 1.43$, the P-value can be found using a standard normal distribution table or a calculator, which gives a P-value of approximately 0.0764. Since the P-value (0.0764) is greater than the significance level $\alpha = 0.05$, we fail to reject the null hypothesis $\mathrm { H } _ { 0 }$.

Question 15

Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject H₀ for the level of significance α.
Right-tailed test
Z = 0.52 $\alpha$ = 0.05
A)0.3015; Fail to reject $\mathrm { H } _ { 0 }$
B)0.0195; Reject $\mathrm { H } _ { 0 }$
C)0.3015; Reject $\mathrm { H } _ { 0 }$
D)0.6030; Fail to reject H $\mathrm { H } _ { 0 }$

Accepted Answer

For a right-tailed test with Z = 0.52, the P-value is the probability of observing a value greater than 0.52 under the standard normal distribution. This P-value can be found using a Z-table or statistical software, and it is approximately 0.3015. Since the P-value (0.3015) is greater than the significance level α = 0.05, we fail to reject the null hypothesis $H_0$.

Question 16

The P-value for a hypothesis test is P = 0.034. Do you reject or fail to reject $\mathrm { H } _ { 0 }$ when the level of significance is $\alpha$ = 0.01?
A)fail to reject $\mathrm { H } _ { 0 }$
B)reject $\mathrm { H } _ { 0 }$
C)not sufficient information to decide

Accepted Answer

The P-value (0.034) is greater than the significance level ($\alpha$ = 0.01), so we fail to reject the null hypothesis ($\mathrm { H } _ { 0 }$).

Question 17

Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject $\mathrm { H } _ { 0 }$ for the level of significance α $\alpha .$ Two-tailed test
Z = -1.63 $\alpha$ α = 0.05
A)0.1032; fail to reject $\mathrm { H } _ { 0 }$
B)0.9484; fail to reject $\mathrm { H } _ { 0 }$
C)0.0516; reject $\mathrm { H } _ { 0 }$
D)0.0516; fail to reject $\mathrm { H } _ { 0 }$

Accepted Answer

The P-value for Z = -1.63 in a two-tailed test is approximately 0.1032. Since 0.1032 > 0.05, we fail to reject $\mathrm { H } _ { 0 }$.

Question 18

Find the critical value and rejection region for the type of z-test with level of significance α $\alpha$ Left-tailed test, α $\alpha = 0.025$
A) $z _ { 0 } = - 1.96 ; z < - 1.96$
B) $\mathrm { z } 0 = - 2.33 ; \mathrm { z } < - 2.33$
C) $z _ { 0 } = - 2.575 ; z < - 2.575$
D) $z _ { 0 } = - 1.645 ; z < - 1.645$

Accepted Answer

For a left-tailed test with $\alpha = 0.025$, the critical value is $z = -1.96$, indicating that the rejection region is $z < -1.96$.

Question 19

Given $\mathrm { H } _ { 0 } : \mathrm { p }$ = 0.85 and α $\alpha$ = 0.10, which level of confidence should you use to test the claim?
A)90%
B)95%
C)99%
D)80%

Accepted Answer

The level of confidence is 1 - α, so for α = 0.10, the confidence level is 1 - 0.10 = 0.90 or 90%.

Question 20

Find the critical value and rejection region for the type of z-test with level of significance α $\alpha .$ Left-tailed test, α $\alpha = 0.05$
A) $z _ { 0 } = - 1.645 ; z < - 1.645$
B) $z _ { 0 } = - 2.33 ; z < - 2.33$
C) $\mathrm { z } _ { 0 } = - 2.575 ; \mathrm { z } < - 2.575$
D) $z _ { 0 } = - 1.96 ; z < - 1.96$

Accepted Answer

For a left-tailed test with $\alpha = 0.05$, the critical value is $z_{0.05} = -1.645$, indicating that the rejection region is $z < -1.645$.

Quiz 7: Hypothesis Testing With One Sample

Find the critical value and rejection region for the type of z-test with level of significance α α\alphaα Two-tailed test, α α=0.10\alpha = 0.10α=0.10

Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject H0\mathrm { H } _ { 0 }H0​ for the level of significance α α\alphaα Left-tailed test Z = -1.83 α\alphaα α = 0.05

Test the claim about the population mean μ\muμ at the level of significance α. Assume the population is normally distributed. Claim: μ>28;α=0.05;σ=1.2\mu > 28 ; \alpha = 0.05 ; \sigma = 1.2μ>28;α=0.05;σ=1.2 Sample statistics: xˉ=28.3,n=50\bar { x } = 28.3 , n = 50xˉ=28.3,n=50

Given H0:μ≥23.5 and α=0.05, \mathrm { H } _ { 0 } : \mu \geq 23.5 \text { and } \alpha = 0.05 \text {, }H0​:μ≥23.5 and α=0.05, which level of confidence should you use to test the claim?

Given H0:μ≤12\mathrm { H } _ { 0 } : \mu \leq 12H0​:μ≤12 for which confidence interval should you reject H0?\mathrm { H } _ { 0 } ?H0​?

Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject H0\mathrm { H } _ { 0 }H0​ for the level of significance α α\alphaα Two-tailed test Z = 1.95 α\alphaα = 0.05

Find the critical value and rejection region for the type of z-test with level of significance α. Two-tailed test, α α=0.01\alpha = 0.01α=0.01

The P-value for a hypothesis test is P = 0.006. Do you reject or fail to reject H0\mathrm { H } _ { 0 }H0​ when the level of significance is α\alphaα α = 0.01?

The P-value for a hypothesis test is P = 0.066. Do you reject or fail to reject H0\mathrm { H } _ { 0 }H0​ when the level of significance is α\alphaα = 0.05?

Given H0:p≥0.45, \mathrm { H } _ { 0 } : \mathrm { p } \geq 0.45 \text {, }H0​:p≥0.45, for which confidence interval should you reject H0?\mathrm { H } _ { 0 } ?H0​?

Find the critical value and rejection region for the type of z-test with level of significance α α2\alpha _ { 2 }α2​ Right-tailed test, α α\alphaα = 0.01

Find the critical value and rejection region for the type of z-test with level of significance α α\alphaα Two-tailed test, α α\alphaα = 0.06

Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject H0\mathrm { H } _ { 0 }H0​ for the level of significance α α.\alpha .α. Left-tailed test Z = -2.05 α\alphaα = 0.05 The test statistic in a left-tailed test is z = -2.05.

Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject H0\mathrm { H } _ { 0 }H0​ for the level of significance α α\alphaα Right-tailed test Z = 1.43 α\alphaα = 0.05

Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject H₀ for the level of significance α. Right-tailed test Z = 0.52 α\alphaα = 0.05

The P-value for a hypothesis test is P = 0.034. Do you reject or fail to reject H0\mathrm { H } _ { 0 }H0​ when the level of significance is α\alphaα = 0.01?

Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject H0\mathrm { H } _ { 0 }H0​ for the level of significance α α.\alpha .α. Two-tailed test Z = -1.63 α\alphaα α = 0.05

Find the critical value and rejection region for the type of z-test with level of significance α α\alphaα Left-tailed test, α α=0.025\alpha = 0.025α=0.025

Given H0:p\mathrm { H } _ { 0 } : \mathrm { p }H0​:p = 0.85 and α α\alphaα = 0.10, which level of confidence should you use to test the claim?

Find the critical value and rejection region for the type of z-test with level of significance α α.\alpha .α. Left-tailed test, α α=0.05\alpha = 0.05α=0.05

Find the critical value and rejection region for the type of z-test with level of significance α $\alpha$ Two-tailed test, α $\alpha = 0.10$

Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject $\mathrm { H } _ { 0 }$ for the level of significance α $\alpha$ Left-tailed test Z = -1.83 $\alpha$ α = 0.05

Test the claim about the population mean $\mu$ at the level of significance α. Assume the population is normally distributed. Claim: $\mu > 28 ; \alpha = 0.05 ; \sigma = 1.2$ Sample statistics: $\bar { x } = 28.3 , n = 50$

Given $\mathrm { H } _ { 0 } : \mu \geq 23.5 \text { and } \alpha = 0.05 \text {, }$ which level of confidence should you use to test the claim?

Given $\mathrm { H } _ { 0 } : \mu \leq 12$ for which confidence interval should you reject $\mathrm { H } _ { 0 } ?$

Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject $\mathrm { H } _ { 0 }$ for the level of significance α $\alpha$ Two-tailed test Z = 1.95 $\alpha$ = 0.05

Find the critical value and rejection region for the type of z-test with level of significance α. Two-tailed test, α $\alpha = 0.01$

The P-value for a hypothesis test is P = 0.006. Do you reject or fail to reject $\mathrm { H } _ { 0 }$ when the level of significance is $\alpha$ α = 0.01?

The P-value for a hypothesis test is P = 0.066. Do you reject or fail to reject $\mathrm { H } _ { 0 }$ when the level of significance is $\alpha$ = 0.05?

Given $\mathrm { H } _ { 0 } : \mathrm { p } \geq 0.45 \text {, }$ for which confidence interval should you reject $\mathrm { H } _ { 0 } ?$

Find the critical value and rejection region for the type of z-test with level of significance α $\alpha _ { 2 }$ Right-tailed test, α $\alpha$ = 0.01

Find the critical value and rejection region for the type of z-test with level of significance α $\alpha$ Two-tailed test, α $\alpha$ = 0.06

Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject $\mathrm { H } _ { 0 }$ for the level of significance α $\alpha .$ Left-tailed test Z = -2.05 $\alpha$ = 0.05 The test statistic in a left-tailed test is z = -2.05.

Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject $\mathrm { H } _ { 0 }$ for the level of significance α $\alpha$ Right-tailed test Z = 1.43 $\alpha$ = 0.05

Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject H₀ for the level of significance α. Right-tailed test Z = 0.52 $\alpha$ = 0.05

The P-value for a hypothesis test is P = 0.034. Do you reject or fail to reject $\mathrm { H } _ { 0 }$ when the level of significance is $\alpha$ = 0.01?

Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject $\mathrm { H } _ { 0 }$ for the level of significance α $\alpha .$ Two-tailed test Z = -1.63 $\alpha$ α = 0.05

Find the critical value and rejection region for the type of z-test with level of significance α $\alpha$ Left-tailed test, α $\alpha = 0.025$

Given $\mathrm { H } _ { 0 } : \mathrm { p }$ = 0.85 and α $\alpha$ = 0.10, which level of confidence should you use to test the claim?

Find the critical value and rejection region for the type of z-test with level of significance α $\alpha .$ Left-tailed test, α $\alpha = 0.05$