Question

A study at Yellowstone National Park found that the percent of the population of grizzly bears that are female is 54%. A statistician feels that this number has increased in recent years and decides to test this claim. She randomly collects a sample of 50 bears throughout the park and finds that 32 of them are female. Does the data back up the statistician's claim? Use $\alpha = .01$. (20 points) 1. Formulate the hypotheses: $H_o$: $H_a$: State the significance level: $\alpha = $ 2. Model the sampling distribution of the proportion: n= x = $\hat{p} = $ Test statistic = Z = (please label on the curve) $\mu_{\hat{p}} = $ $\sigma_{\hat{p}} = $ 3. P-value = (please label on the curve) 4. Decision Rule: Reject $H_o$ if < 5. Sate your conclusion: Since the p-value is than $\alpha$, we $H_o$. We can conclude that:

          A study at Yellowstone National Park found that the percent of the population of grizzly bears that are
female is 54%. A statistician feels that this number has increased in recent years and decides to test this
claim. She randomly collects a sample of 50 bears throughout the park and finds that 32 of them are
female. Does the data back up the statistician's claim? Use $\alpha = .01$.
(20 points)
1. Formulate the hypotheses:
$H_o$:
$H_a$:
State the significance level: $\alpha = $
2. Model the sampling distribution of the proportion:
n=
x =
$\hat{p} = $
Test statistic = Z = 
(please label on the curve)
$\mu_{\hat{p}} = $
$\sigma_{\hat{p}} = $
3. P-value = 
(please label on the curve)
4. Decision Rule:
Reject $H_o$ if
< 
5. Sate your conclusion:
Since the p-value is
than $\alpha$, we
$H_o$.
We can conclude that:

Show more…

A study at Yellowstone National Park found that the percent of the population of grizzly bears that are
female is 54%. A statistician feels that this number has increased in recent years and decides to test this
claim. She randomly collects a sample of 50 bears throughout the park and finds that 32 of them are
female. Does the data back up the statistician's claim? Use α = .01.
(20 points)
1. Formulate the hypotheses:
Ho:
Ha:
State the significance level: α =
2. Model the sampling distribution of the proportion:
n=
x =
p̂ =
Test statistic = Z =
(please label on the curve)
μp̂ =
σp̂ =
3. P-value =
(please label on the curve)
4. Decision Rule:
Reject Ho if
<
5. Sate your conclusion:
Since the p-value is
than α, we
Ho.
We can conclude that:

Added by Stephanie R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

05/15/2023

Step 1

The alternative hypothesis is that the proportion of female grizzly bears is greater than 54%. Show more…

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A study at Yellowstone National Park found that the percent of the population of grizzly bears that are female is 54%. A statistician feels that this number has increased in recent years and decides to test this claim. She randomly collects a sample of 50 bears throughout the park and finds that 32 of them are female. Does the data back up the statistician's claim? Use a = .01. (20 points) 1. Formulate the hypotheses: Ho: Ha: State the significance level: a = 2. Model the sampling distribution of the proportion: n= x = p = Test statistic = Z = (please label on the curve) μ = σρ = 3. P-value = (please label on the curve) 4. Decision Rule: Reject Ho if < 5. Sate your conclusion: Since the p-value is than a, we Ho. We can conclude that:

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Transcript

00:01 Let's solve this question.

00:01 In this question we have given that the sample size n is equal to 49, x bar is equal to 182 .9, standard deviation s is equal to 121 .8.

00:16 Now here in the part a we need to find the null and alternative hypothesis that is equal to question mark.

00:23 In the part b we need to find the point estimate x bar is equal to question mark.

00:28 In the part c we need to find the standard error se that is equal to question mark.

00:35 In the part d we need to find the test statistic that is equal to question mark.

00:45 In the part e we need to find the p value and in the part f we need to find the conclusion whether the null hypothesis is rejected or not.

01:02 So here first of all for the part a we can say that here the null hypothesis h0 such that that is mu is equal to 200 versus the alternative hypothesis h such that mu is not equal to 200.

01:18 So this will be the required answer for the part a.

01:21 Now here for the part b here we need to find the point estimate.

01:27 So here the point estimate that can be given as that is equal to the mean that is x bar that is equal to 182 .9.

01:35 So this will be the answer for the part b.

01:38 Now for the part c we need to find the standard error that is given as s divided by square root of n so that is equal to 121 .8 divided by square root of 49 so that is equal to we will get 17 .4...

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