Math / Data & Statistics

QuestionFind the P-value for the indicated hypothesis test with the given standardized test statistic, $z$ . Decide whether to reject $H_0$ for the given level of significance $\alpha$ . Right-tailed test with test statistic $z = 1.39$ and $\alpha = 0.04$ . P-value = (Round to four decimal places as needed.)

Studdy Solution

STEP 1

What is this asking? We need to find the probability of getting a test statistic as extreme as $z = 1.39$ if the null hypothesis is true, and then decide if that's small enough to reject the null hypothesis given our significance level of $\alpha = 0.04$ . Watch out! Make sure you're looking at the correct tail of the distribution – this is a right-tailed test!

STEP 2

1. Find the p-value.
2. Compare to alpha.

STEP 3

For a right-tailed test, the p-value is the probability of observing a $z$ -score greater than or equal to our test statistic, assuming the null hypothesis is true.
In this case, we want $P(Z \ge 1.39)$ .

STEP 4

We can use a $z$ -table or technology to find $P(Z < 1.39)$ .
Let's say we find that $P(Z < 1.39) = 0.9177$ .

STEP 5

Since the total probability under the standard normal curve is 1, we can find the probability in the right tail by subtracting the value we just found from 1: $P(Z \ge 1.39) = 1 - P(Z < 1.39) = 1 - 0.9177 = \textbf{0.0823}$ So, our p-value is 0.0823.

STEP 6

Our significance level, $\alpha$ , is 0.04.
This is the threshold we've set for deciding whether to reject the null hypothesis.

STEP 7

Our p-value (0.0823) is greater than $\textbf{0.04}$ .

STEP 8

Since our p-value is greater than alpha, we fail to reject the null hypothesis.
There's not enough evidence to reject it at the $\alpha = 0.04$ significance level.

STEP 9

P-value = 0.0823.
We fail to reject $H_0$ .

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Studdy Solution

STEP 1

STEP 2

1. Find the p-value.
2. Compare to alpha.

STEP 3

For a right-tailed test, the p-value is the probability of observing a $z$ -score greater than or equal to our test statistic, assuming the null hypothesis is true.
In this case, we want $P(Z \ge 1.39)$ .

STEP 4

We can use a $z$ -table or technology to find $P(Z < 1.39)$ .
Let's say we find that $P(Z < 1.39) = 0.9177$ .

STEP 5

Since the total probability under the standard normal curve is 1, we can find the probability in the right tail by subtracting the value we just found from 1: $P(Z \ge 1.39) = 1 - P(Z < 1.39) = 1 - 0.9177 = \textbf{0.0823}$ So, our p-value is 0.0823.

STEP 6

Our significance level, $\alpha$ , is 0.04.
This is the threshold we've set for deciding whether to reject the null hypothesis.

STEP 7

Our p-value (0.0823) is greater than $\textbf{0.04}$ .

STEP 8

Since our p-value is greater than alpha, we fail to reject the null hypothesis.
There's not enough evidence to reject it at the $\alpha = 0.04$ significance level.

STEP 9

P-value = 0.0823.
We fail to reject $H_0$ .

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Studdy Solution

STEP 1

STEP 2

1. Find the p-value.2. Compare to alpha.

STEP 3

For a right-tailed test, the p-value is the probability of observing a zzz-score *greater than or equal to* our test statistic, assuming the null hypothesis is true.In this case, we want P(Z≥1.39)P(Z \ge 1.39)P(Z≥1.39).

STEP 4

We can use a zzz-table or technology to find P(Z<1.39)P(Z < 1.39)P(Z<1.39).Let's say we find that P(Z<1.39)=0.9177P(Z < 1.39) = 0.9177P(Z<1.39)=0.9177.

STEP 5

STEP 6

Our significance level, α\alphaα, is **0.04**.This is the threshold we've set for deciding whether to reject the null hypothesis.

STEP 7

Our **p-value (0.0823)** is *greater than* 0.04\textbf{0.04}0.04.

STEP 8

Since our p-value is greater than alpha, we *fail to reject* the null hypothesis.There's not enough evidence to reject it at the α=0.04\alpha = 0.04α=0.04 significance level.

STEP 9

P-value = 0.0823.We fail to reject H0H_0H0​.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Find the p-value.
2. Compare to alpha.

For a right-tailed test, the p-value is the probability of observing a $z$ -score greater than or equal to our test statistic, assuming the null hypothesis is true.
In this case, we want $P(Z \ge 1.39)$ .

We can use a $z$ -table or technology to find $P(Z < 1.39)$ .
Let's say we find that $P(Z < 1.39) = 0.9177$ .

Our significance level, $\alpha$ , is 0.04.
This is the threshold we've set for deciding whether to reject the null hypothesis.

Our p-value (0.0823) is greater than $\textbf{0.04}$ .

Since our p-value is greater than alpha, we fail to reject the null hypothesis.
There's not enough evidence to reject it at the $\alpha = 0.04$ significance level.

P-value = 0.0823.
We fail to reject $H_0$ .