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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) 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?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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. +=+
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.
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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Certainly! Here's a transcription of the text that can be used on an educational website: --- **Hypothesis Testing** **Options:** - ○ 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. **b-1. Calculation:** 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:** [Input box] **b-2. Find the p-value.** - ○ 0.05 ≤ p-value < 0.10 - ○ p-value ≥ 0.10 - ○ p-value < 0.01 - ○ 0.01 ≤ p-value < 0.025 - ○ 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. - ○ No, since the value of the p-value is less than the significance level. **b-4. Interpret the results at α = 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. --- This transcription provides a clear and structured format for educational purposes, explaining the steps of hypothesis testing including calculation, p-value determination, hypothesis rejection, and result interpretation.
Transcribed Image Text:Certainly! Here's a transcription of the text that can be used on an educational website: --- **Hypothesis Testing** **Options:** - ○ 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. **b-1. Calculation:** 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:** [Input box] **b-2. Find the p-value.** - ○ 0.05 ≤ p-value < 0.10 - ○ p-value ≥ 0.10 - ○ p-value < 0.01 - ○ 0.01 ≤ p-value < 0.025 - ○ 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. - ○ No, since the value of the p-value is less than the significance level. **b-4. Interpret the results at α = 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. --- This transcription provides a clear and structured format for educational purposes, explaining the steps of hypothesis testing including calculation, p-value determination, hypothesis rejection, and result interpretation.
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