Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. (You may find it useful to reference the appropriate table: z table or ttable) H2 20 He: H1 HA: H1 H2 < 0 x₁ = 267 $1 = 37 n₁ = 11 22 = 295 $2 = 31 n2 = 11 a-1. Calculate the value of the test statistic under the assumption that the population variances are equal. (Negative value should be indicated by a minus sign. Round final answer to 3 decimal places.) Test statistic a-2. Find the p-value. O 0.05 s p-value < 0.10 O p-value ≥ 0.10 O p-value < 0.01 O 0.01 s p-value < 0.025 O 0.025 s p-value < 0.05 a-3. Do you reject the pull hypothesis at the 1% level?
Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. (You may find it useful to reference the appropriate table: z table or ttable) H2 20 He: H1 HA: H1 H2 < 0 x₁ = 267 $1 = 37 n₁ = 11 22 = 295 $2 = 31 n2 = 11 a-1. Calculate the value of the test statistic under the assumption that the population variances are equal. (Negative value should be indicated by a minus sign. Round final answer to 3 decimal places.) Test statistic a-2. Find the p-value. O 0.05 s p-value < 0.10 O p-value ≥ 0.10 O p-value < 0.01 O 0.01 s p-value < 0.025 O 0.025 s p-value < 0.05 a-3. Do you reject the pull hypothesis at the 1% level?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section: Chapter Questions
Problem 8SGR
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![Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed
populations. (You may find it useful to reference the appropriate table: z table or ttable)
HØ: H1
HA: H1
-
μ2 20
H2 < 0
x1 = 267
$1 = 37
n1 = 11
x2 = 295
52 = 31
n2 = 11
a-1. Calculate the value of the test statistic under the assumption that the population variances are equal. (Negative value should be
indicated by a minus sign. Round final answer to 3 decimal places.)
Test statistic
a-2. Find the p-value.
O 0.05 ≤ p-value < 0.10
p-value > 0.10
O p-value < 0.01
0.01 s p-value < 0.025
O 0.025 ≤ p-value < 0.05
a-3. Do you reject the null hypothesis at the 1% level?
Yes, since the value of the p-value is less than the significance level.
No, since the value of the p-value is less than the significance level.
No, since the value of the p-value is greater than the significance level.
Yes, since the value of the p-value is greater than the significance level.
a-4. Interpret the results at a = 0.01.
We conclude that the population means differ.
We cannot conclude that the population means differ.
We conclude that population mean 1 is less than population mean 2.
+=+](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F21d4eb06-eaa2-4705-83a6-21563ae4212f%2Faa7da962-877a-4fb4-b4db-8e7d33501b08%2Fykeddt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed
populations. (You may find it useful to reference the appropriate table: z table or ttable)
HØ: H1
HA: H1
-
μ2 20
H2 < 0
x1 = 267
$1 = 37
n1 = 11
x2 = 295
52 = 31
n2 = 11
a-1. Calculate the value of the test statistic under the assumption that the population variances are equal. (Negative value should be
indicated by a minus sign. Round final answer to 3 decimal places.)
Test statistic
a-2. Find the p-value.
O 0.05 ≤ p-value < 0.10
p-value > 0.10
O p-value < 0.01
0.01 s p-value < 0.025
O 0.025 ≤ p-value < 0.05
a-3. Do you reject the null hypothesis at the 1% level?
Yes, since the value of the p-value is less than the significance level.
No, since the value of the p-value is less than the significance level.
No, since the value of the p-value is greater than the significance level.
Yes, since the value of the p-value is greater than the significance level.
a-4. Interpret the results at a = 0.01.
We conclude that the population means differ.
We cannot conclude that the population means differ.
We conclude that population mean 1 is less than population mean 2.
+=+
![O We cannot conclude that the population means differ.
We conclude that population mean 1 is less than population mean 2.
O We cannot conclude that population mean 1 is less than population mean 2.
b-1. Calculate the value of the test statistic under the assumption that the population variances are unknown and are not equal.
(Negative value should be indicated by a minus sign. Round final answer to 3 decimal places.)
Test statistic
b-2. Find the p-value.
0.05 ≤ p-value < 0.10
p-value > 0.10
p-value < 0.01
O 0.01 ≤ p-value < 0.025
O 0.025 ≤ p-value < 0.05
b-3. Do you reject the null hypothesis at the 1% level?
Yes, since the value of the p-value is less than the significance level.
No, since the value of the p-value is greater than the significance level.
Yes, since the value of the p-value is greater than the significance level.
O No, since the value of the p-value is less than the significance level.
b-4. Interpret the results at a = 0.01.
We conclude that the population means differ.
We cannot conclude that the population means differ.
We conclude that population mean 1 is less than population mean 2.
We cannot conclude that population mean 1 is less than population mean 2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F21d4eb06-eaa2-4705-83a6-21563ae4212f%2Faa7da962-877a-4fb4-b4db-8e7d33501b08%2F8w6q9w8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:O We cannot conclude that the population means differ.
We conclude that population mean 1 is less than population mean 2.
O We cannot conclude that population mean 1 is less than population mean 2.
b-1. Calculate the value of the test statistic under the assumption that the population variances are unknown and are not equal.
(Negative value should be indicated by a minus sign. Round final answer to 3 decimal places.)
Test statistic
b-2. Find the p-value.
0.05 ≤ p-value < 0.10
p-value > 0.10
p-value < 0.01
O 0.01 ≤ p-value < 0.025
O 0.025 ≤ p-value < 0.05
b-3. Do you reject the null hypothesis at the 1% level?
Yes, since the value of the p-value is less than the significance level.
No, since the value of the p-value is greater than the significance level.
Yes, since the value of the p-value is greater than the significance level.
O No, since the value of the p-value is less than the significance level.
b-4. Interpret the results at a = 0.01.
We conclude that the population means differ.
We cannot conclude that the population means differ.
We conclude that population mean 1 is less than population mean 2.
We cannot conclude that population mean 1 is less than population mean 2.
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Follow-up Question
![O We cannot conclude that the population means differ.
We conclude that population mean 1 is less than population mean 2.
O We cannot conclude that population mean 1 is less than population mean 2.
b-1. Calculate the value of the test statistic under the assumption that the population variances are unknown and are not equal.
(Negative value should be indicated by a minus sign. Round final answer to 3 decimal places.)
Test statistic
b-2. Find the p-value.
0.05 ≤ p-value < 0.10
p-value > 0.10
p-value < 0.01
O 0.01 ≤ p-value < 0.025
O 0.025 ≤ p-value < 0.05
b-3. Do you reject the null hypothesis at the 1% level?
Yes, since the value of the p-value is less than the significance level.
No, since the value of the p-value is greater than the significance level.
Yes, since the value of the p-value is greater than the significance level.
O No, since the value of the p-value is less than the significance level.
b-4. Interpret the results at a = 0.01.
We conclude that the population means differ.
We cannot conclude that the population means differ.
We conclude that population mean 1 is less than population mean 2.
We cannot conclude that population mean 1 is less than population mean 2.](https://content.bartleby.com/qna-images/question/21d4eb06-eaa2-4705-83a6-21563ae4212f/6a661642-6ee8-422c-b598-4151f1593296/j6vs87r_thumbnail.jpeg)
Transcribed Image Text:O We cannot conclude that the population means differ.
We conclude that population mean 1 is less than population mean 2.
O We cannot conclude that population mean 1 is less than population mean 2.
b-1. Calculate the value of the test statistic under the assumption that the population variances are unknown and are not equal.
(Negative value should be indicated by a minus sign. Round final answer to 3 decimal places.)
Test statistic
b-2. Find the p-value.
0.05 ≤ p-value < 0.10
p-value > 0.10
p-value < 0.01
O 0.01 ≤ p-value < 0.025
O 0.025 ≤ p-value < 0.05
b-3. Do you reject the null hypothesis at the 1% level?
Yes, since the value of the p-value is less than the significance level.
No, since the value of the p-value is greater than the significance level.
Yes, since the value of the p-value is greater than the significance level.
O No, since the value of the p-value is less than the significance level.
b-4. Interpret the results at a = 0.01.
We conclude that the population means differ.
We cannot conclude that the population means differ.
We conclude that population mean 1 is less than population mean 2.
We cannot conclude that population mean 1 is less than population mean 2.
Solution
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