AP Statistics - Significance

1

A study would like to determine whether meditation helps students improve focus time. They used a control group of 30 students and compared their focus time to a group of 30 meditating students and compared their average time spent meditating. What is the appropriate null hypothesis for this study?

$\mu_c_o_n_t_r_o_l - \mu_m_e_d_i_t_a_t_o_r_s \geq 0$

$\mu_c_o_n_t_r_o_l - \mu_m_e_d_i_t_a_t_o_r_s > 0$

$\mu_c_o_n_t_r_o_l - \mu_m_e_d_i_t_a_t_o_r_s \leq 0$

$\mu_c_o_n_t_r_o_l - \mu_m_e_d_i_t_a_t_o_r_s < 30$

Explanation

Because we are comparing two samples, the hypothesis takes the form of Mu1- Mu2. Because we are testing the claim that meditation increases average study time, the null hypothesis must cover all other outcomes. That means the null hypothesis is that the difference between control minus meditation is greater than or equal to zero.

2

A study would like to determine whether meditation helps students improve focus time. They used a control group of 30 students and compared their focus time to a group of 30 meditating students and compared their average time spent meditating. What is the appropriate null hypothesis for this study?

$\mu_c_o_n_t_r_o_l - \mu_m_e_d_i_t_a_t_o_r_s \geq 0$

$\mu_c_o_n_t_r_o_l - \mu_m_e_d_i_t_a_t_o_r_s > 0$

$\mu_c_o_n_t_r_o_l - \mu_m_e_d_i_t_a_t_o_r_s \leq 0$

$\mu_c_o_n_t_r_o_l - \mu_m_e_d_i_t_a_t_o_r_s < 30$

Explanation

Because we are comparing two samples, the hypothesis takes the form of Mu1- Mu2. Because we are testing the claim that meditation increases average study time, the null hypothesis must cover all other outcomes. That means the null hypothesis is that the difference between control minus meditation is greater than or equal to zero.

3

A study would like to determine whether meditation helps students improve focus time. They used a control group of 30 students and compared their focus time to a group of 30 meditating students and compared their average time spent meditating. What is the appropriate null hypothesis for this study?

$\mu_c_o_n_t_r_o_l - \mu_m_e_d_i_t_a_t_o_r_s \geq 0$

$\mu_c_o_n_t_r_o_l - \mu_m_e_d_i_t_a_t_o_r_s > 0$

$\mu_c_o_n_t_r_o_l - \mu_m_e_d_i_t_a_t_o_r_s \leq 0$

$\mu_c_o_n_t_r_o_l - \mu_m_e_d_i_t_a_t_o_r_s < 30$

Explanation

Because we are comparing two samples, the hypothesis takes the form of Mu1- Mu2. Because we are testing the claim that meditation increases average study time, the null hypothesis must cover all other outcomes. That means the null hypothesis is that the difference between control minus meditation is greater than or equal to zero.

4

A study would like to determine whether meditation helps students improve focus time. They know that the average focus time of an American 4th grader is 23 minutes. They then recruit 50 meditators and calculate their average focus time. What is the appropriate null hypothesis for this study?

$\mu \leq 23$

$\mu < 23$

$\mu > 23$

$\mu \leq 50$

$\mu > 50$

Explanation

Because we are comparing one sample to a known mean, the hypothesis is $\mu$ compared to the known average, 23. We would like to test the claim that meditating will increase focus time, therefore our null hypothesis must include all other outcomes. Therefore, the null is that Mu is less than or equal to 23.

5

If a hypothesis test uses a confidence level, then what is its probability of Type I Error?

Explanation

By definition, the probability of Type I Error is,

$P(E_{TI})=1-C$

where,

$P(E_{TI})$ represents Probability of Type I Error and represents the confidence level.

Thus resulting in:

$P(E_{TI})=1-.95=0.05$

6

A prominent football coach is being reviewed for his performance in the past season. To evaluate how well the coach has done, the team manager runs a statistical test comparing the coach to a sample of coaches in the league. If the test suggests that the coach outperformed other coaches when in fact he did not, and the manager then rejects the null hypothesis (that the coach did not outperform the other coaches), what kind of error is he committing?

Type I error

Type II error

Type M error

None of the above

Explanation

A type I error occurs when one rejects a null hypothesis that is in fact true. The null hypothesis is that the coach does not outperform other coaches, and the test reccomends that we reject it even though it is true. Thus, a type I error has been committed.

7

A study would like to determine whether meditation helps students improve focus time. They know that the average focus time of an American 4th grader is 23 minutes. They then recruit 50 meditators and calculate their average focus time. What is the appropriate null hypothesis for this study?

$\mu \leq 23$

$\mu < 23$

$\mu > 23$

$\mu \leq 50$

$\mu > 50$

Explanation

Because we are comparing one sample to a known mean, the hypothesis is $\mu$ compared to the known average, 23. We would like to test the claim that meditating will increase focus time, therefore our null hypothesis must include all other outcomes. Therefore, the null is that Mu is less than or equal to 23.

8

If a hypothesis test uses a confidence level, then what is its probability of Type I Error?

Explanation

By definition, the probability of Type I Error is,

$P(E_{TI})=1-C$

where,

$P(E_{TI})$ represents Probability of Type I Error and represents the confidence level.

Thus resulting in:

$P(E_{TI})=1-.95=0.05$

9

A study would like to determine whether meditation helps students improve focus time. They know that the average focus time of an American 4th grader is 23 minutes. They then recruit 50 meditators and calculate their average focus time. What is the appropriate null hypothesis for this study?

$\mu \leq 23$

$\mu < 23$

$\mu > 23$

$\mu \leq 50$

$\mu > 50$

Explanation

Because we are comparing one sample to a known mean, the hypothesis is $\mu$ compared to the known average, 23. We would like to test the claim that meditating will increase focus time, therefore our null hypothesis must include all other outcomes. Therefore, the null is that Mu is less than or equal to 23.

10

A prominent football coach is being reviewed for his performance in the past season. To evaluate how well the coach has done, the team manager runs a statistical test comparing the coach to a sample of coaches in the league. If the test suggests that the coach outperformed other coaches when in fact he did not, and the manager then rejects the null hypothesis (that the coach did not outperform the other coaches), what kind of error is he committing?

Type I error

Type II error

Type M error

None of the above

Explanation

A type I error occurs when one rejects a null hypothesis that is in fact true. The null hypothesis is that the coach does not outperform other coaches, and the test reccomends that we reject it even though it is true. Thus, a type I error has been committed.

Significance

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