Solved on Nov 05, 2023

Find the critical value(s) for the left-tailed $t$ -test with $\alpha=0.025$ and $n=27$ . The critical value(s) is/are $t_{\alpha, n-1}$ .

STEP 1

Assumptions1. The test is left-tailed. The level of significance, $\alpha$ , is0.0253. The sample size, $n$ , is274. We are using the t-distribution table

STEP 2

To find the critical value, we need to use the t-distribution table. The degrees of freedom for the t-distribution is given by $n -1$ , where $n$ is the sample size.
$df = n -1$

STEP 3

Now, plug in the given value for the sample size to calculate the degrees of freedom.
$df =27 -1$

STEP 4

Calculate the degrees of freedom.
$df =27 -1 =26$

STEP 5

Now that we have the degrees of freedom, we can find the critical value from the t-distribution table. The critical value is the t-score that corresponds to the given level of significance, $\alpha$ , and degrees of freedom, $df$ .

STEP 6

Look up the critical value in the t-distribution table for $df =26$ and $\alpha =0.025$ . Since this is a left-tailed test, we are looking for the negative t-score.

STEP 7

The critical value from the t-distribution table for $df =26$ and $\alpha =0.025$ is approximately $-2.056$ .
The critical value(s) is/are $-2.056$ .

STEP 8

The rejection region for a left-tailed test is all values less than the critical value. So, the rejection region is $t < -2.056$ .

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Find the critical value(s) for the left-tailed $t$ -test with $\alpha=0.025$ and $n=27$ . The critical value(s) is/are $t_{\alpha, n-1}$ .

STEP 1

Assumptions1. The test is left-tailed. The level of significance, $\alpha$ , is0.0253. The sample size, $n$ , is274. We are using the t-distribution table

STEP 2

To find the critical value, we need to use the t-distribution table. The degrees of freedom for the t-distribution is given by $n -1$ , where $n$ is the sample size.
$df = n -1$

STEP 3

Now, plug in the given value for the sample size to calculate the degrees of freedom.
$df =27 -1$

STEP 4

Calculate the degrees of freedom.
$df =27 -1 =26$

STEP 5

Now that we have the degrees of freedom, we can find the critical value from the t-distribution table. The critical value is the t-score that corresponds to the given level of significance, $\alpha$ , and degrees of freedom, $df$ .

STEP 6

Look up the critical value in the t-distribution table for $df =26$ and $\alpha =0.025$ . Since this is a left-tailed test, we are looking for the negative t-score.

STEP 7

The critical value from the t-distribution table for $df =26$ and $\alpha =0.025$ is approximately $-2.056$ .
The critical value(s) is/are $-2.056$ .

STEP 8

The rejection region for a left-tailed test is all values less than the critical value. So, the rejection region is $t < -2.056$ .

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Find the critical value(s) for the left-tailed ttt-test with α=0.025\alpha=0.025α=0.025 and n=27n=27n=27. The critical value(s) is/are tα,n−1t_{\alpha, n-1}tα,n−1​.

STEP 1

Assumptions1. The test is left-tailed. The level of significance, α\alphaα, is0.0253. The sample size, nnn, is274. We are using the t-distribution table

STEP 2

To find the critical value, we need to use the t-distribution table. The degrees of freedom for the t-distribution is given by n−1n -1n−1, where nnn is the sample size.df=n−1df = n -1df=n−1

STEP 3

Now, plug in the given value for the sample size to calculate the degrees of freedom.df=27−1df =27 -1df=27−1

STEP 4

Calculate the degrees of freedom.df=27−1=26df =27 -1 =26df=27−1=26

STEP 5

Now that we have the degrees of freedom, we can find the critical value from the t-distribution table. The critical value is the t-score that corresponds to the given level of significance, α\alphaα, and degrees of freedom, dfdfdf.

STEP 6

Look up the critical value in the t-distribution table for df=26df =26df=26 and α=0.025\alpha =0.025α=0.025. Since this is a left-tailed test, we are looking for the negative t-score.

STEP 7

The critical value from the t-distribution table for df=26df =26df=26 and α=0.025\alpha =0.025α=0.025 is approximately −2.056-2.056−2.056.The critical value(s) is/are −2.056-2.056−2.056.

STEP 8

The rejection region for a left-tailed test is all values less than the critical value. So, the rejection region is t<−2.056t < -2.056t<−2.056.

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Find the critical value(s) for the left-tailed $t$ -test with $\alpha=0.025$ and $n=27$ . The critical value(s) is/are $t_{\alpha, n-1}$ .

Assumptions1. The test is left-tailed. The level of significance, $\alpha$ , is0.0253. The sample size, $n$ , is274. We are using the t-distribution table

To find the critical value, we need to use the t-distribution table. The degrees of freedom for the t-distribution is given by $n -1$ , where $n$ is the sample size.
$df = n -1$

Now, plug in the given value for the sample size to calculate the degrees of freedom.
$df =27 -1$

Calculate the degrees of freedom.
$df =27 -1 =26$

Now that we have the degrees of freedom, we can find the critical value from the t-distribution table. The critical value is the t-score that corresponds to the given level of significance, $\alpha$ , and degrees of freedom, $df$ .

Look up the critical value in the t-distribution table for $df =26$ and $\alpha =0.025$ . Since this is a left-tailed test, we are looking for the negative t-score.

The critical value from the t-distribution table for $df =26$ and $\alpha =0.025$ is approximately $-2.056$ .
The critical value(s) is/are $-2.056$ .

The rejection region for a left-tailed test is all values less than the critical value. So, the rejection region is $t < -2.056$ .