91影视

The null hypothesis, denoted by H₀, is the claim that is initially assumed to be true (the 鈥減rior belief鈥� claim). The alternative hypothesis, denoted by H_a, is the assertion that is contradictory to H₀.

The null hypothesis will be rejected in favour of the alternative hypothesis only if sample evidence suggests that H₀ is false. If the sample does not strongly contradict H₀, we will continue to believe in the plausibility of the null hypothesis. The two possible conclusions from a hypothesis-testing analysis are then reject H0 or fail to reject H₀.

Given that,

\(z = 2.10\)

Given claim: \(\mu \) differs from the target value of \(30psi\)

The null hypothesis states that the population mean \(\mu \) is equal to the value mentioned in the given claim:

\({H_0}:\mu = 30psi\)

The alternative hypothesis states the given claim:

\({H_a}:\mu \ne 30psi\)

The P-value is the probability of obtaining a value more extreme or equal to the standardized test statistic z.

Since the alternative hypothesis states , \({H_a}:\mu \ne 30psi\), the P-value is the probability to the left of the negative absolute value of the z-score and to the right of the positive absolute value of the z-score.

Determine the probability using normal probability table in the appendix, which contains the probability to the left of z-scores(use the complement rule),

\(\begin{array}{l}P = P(Z < - 2.10orZ > 2.10)\\ = 2P(Z < - 2.10)\\ = 2(0.0179)\\ = 0.0358\end{array}\)

\(P = 3.58\% \)

Given that,

\(z = - 1.75\)

Given claim: \(\mu \) differs from the target value of \(30psi\)

The null hypothesis states that the population mean \(\mu \) is equal to the value mentioned in the given claim:

\({H_0}:\mu = 30psi\)

The alternative hypothesis states the given claim:

\({H_a}:\mu \ne 30psi\)

The P-value is the probability of obtaining a value more extreme or equal to the standardized test statistic z.

Since the alternative hypothesis states , \({H_a}:\mu \ne 30psi\), the P-value is the probability to the left of the negative absolute value of the z-score and to the right of the positive absolute value of the z-score.

Determine the probability using normal probability table in the appendix, which contains the probability to the left of z-scores(use the complement rule),

\(\begin{array}{l}P = P(Z < - 1.75orZ > 1.75)\\ = 2P(Z < - 1.75)\\ = 2(0.0401)\\ = 0.0802\end{array}\)

\(P = 8.02\% \)

Given that,

\(z = - 0.55\)

Given claim: \(\mu \) differs from the target value of \(30psi\)

The null hypothesis states that the population mean \(\mu \) is equal to the value mentioned in the given claim:

\({H_0}:\mu = 30psi\)

The alternative hypothesis states the given claim:

\({H_a}:\mu \ne 30psi\)

The P-value is the probability of obtaining a value more extreme or equal to the standardized test statistic z.

Since the alternative hypothesis states , \({H_a}:\mu \ne 30psi\), the P-value is the probability to the left of the negative absolute value of the z-score and to the right of the positive absolute value of the z-score.

Determine the probability using normal probability table in the appendix, which contains the probability to the left of z-scores(use the complement rule),

\(\begin{array}{l}P = P(Z < - 0.55orZ > 0.55)\\ = 2P(Z < - 0.55)\\ = 2(0.2912)\\ = 0.5824\end{array}\)

\(P = 58.24\% \)

Given that,

\(z = 1.41\)

Given claim: \(\mu \) differs from the target value of \(30psi\)

The null hypothesis states that the population mean \(\mu \) is equal to the value mentioned in the given claim:

\({H_0}:\mu = 30psi\)

The alternative hypothesis states the given claim:

\({H_a}:\mu \ne 30psi\)

The P-value is the probability of obtaining a value more extreme or equal to the standardized test statistic z.

Since the alternative hypothesis states , \({H_a}:\mu \ne 30psi\), the P-value is the probability to the left of the negative absolute value of the z-score and to the right of the positive absolute value of the z-score.

Determine the probability using normal probability table in the appendix, which contains the probability to the left of z-scores(use the complement rule),

\(\begin{array}{l}P = P(Z < - 1.41orZ > 1.41)\\ = 2P(Z < - 1.41)\\ = 2(0.0793)\\ = 0.1586\end{array}\)

\(P = 15.86\% \)

Given that,

\(z = - 5.30\)

Given claim: \(\mu \) differs from the target value of \(30psi\)

The null hypothesis states that the population mean \(\mu \) is equal to the value mentioned in the given claim:

\({H_0}:\mu = 30psi\)

The alternative hypothesis states the given claim:

\({H_a}:\mu \ne 30psi\)

The P-value is the probability of obtaining a value more extreme or equal to the standardized test statistic z.

Since the alternative hypothesis states , \({H_a}:\mu \ne 30psi\), the P-value is the probability to the left of the negative absolute value of the z-score and to the right of the positive absolute value of the z-score.

Determine the probability using normal probability table in the appendix, which contains the probability to the left of z-scores(use the complement rule),

\(\begin{array}{l}P = P(Z < - 5.30orZ > 5.30)\\ = 2P(Z < - 5.30)\\ \approx 2(0)\\P \approx 0\end{array}\)

\(P \approx 0\)