You have been asked to determine if two different production processes have different mean numbers of units produced per hour. Process 1 has a mean defined as μ₁ and process 2 has a mean defined as μ2. The null and alternative hypotheses are H₂: μ₁ −μ₂ ≤0 and H₁: ₁-₂ > 0. The process variances are unknown but assumed to be equal. Using random samples of 36 observations from process 1 and 49 observations from process 2, the sample means are 60 and 50 for populations 1 and 2 respectively. Complete parts a through d below. Click the icon to view a table of critical values for the Student's t-distribution. a. Can you reject the null hypothesis, using a probability of Type I error x = 0.05, if the sample standard deviation from process 1 is 28 and from process 2 is 23? The test statistic is t=. (Round to three decimal places as needed.)

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You have been asked to determine if two different production processes have different mean numbers of units produced per hour.
Process 1 has a mean defined as µ₁ and process 2 has a mean defined as µ2. The null and alternative hypotheses are Hỏ: µ₁ −µ₂ ≤0
and H₁: ₁-₂ > 0. The process variances are unknown but assumed to be equal. Using random samples of 36 observations from
process 1 and 49 observations from process 2, the sample means are 60 and 50 for populations 1 and 2 respectively. Complete parts a
through d below.
Click the icon to view a table of critical values for the Student's t-distribution.
a. Can you reject the null hypothesis, using a probability of Type I error x = 0.05, if the sample standard deviation from process 1 is 28
and from process 2 is 23?
The test statistic is t =
(Round to three decimal places as needed.)
Transcribed Image Text:You have been asked to determine if two different production processes have different mean numbers of units produced per hour. Process 1 has a mean defined as µ₁ and process 2 has a mean defined as µ2. The null and alternative hypotheses are Hỏ: µ₁ −µ₂ ≤0 and H₁: ₁-₂ > 0. The process variances are unknown but assumed to be equal. Using random samples of 36 observations from process 1 and 49 observations from process 2, the sample means are 60 and 50 for populations 1 and 2 respectively. Complete parts a through d below. Click the icon to view a table of critical values for the Student's t-distribution. a. Can you reject the null hypothesis, using a probability of Type I error x = 0.05, if the sample standard deviation from process 1 is 28 and from process 2 is 23? The test statistic is t = (Round to three decimal places as needed.)
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Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question
You have been asked to determine if two different production processes have different mean numbers of units produced per hour. Process 1 has a mean
defined as μ₁ and process 2 has a mean defined as µ₂. The null and alternative hypotheses are H₂: μ₁ −μ₂ ≤0 and H₁ : µ₁ − µ₂ > 0. The process variances
are unknown but assumed to be equal. Using random samples of 36 observations from process 1 and 49 observations from process 2, the sample means are
60 and 50 for populations 1 and 2 respectively. Complete parts a through d below.
Click the icon to view a table of critical values for the Student's t-distribution.
THIV IVVI VIMUVUV IVA
Since the test statistic is
IV
The test statistic is t =
MITM IV
ܝ
The critical value(s) is(are) 1.663.
(Round to three decimal places as needed. Use a comma to separate answers as needed.)
greater than t + ny – 2,0 ²
reject Ho.
c. Can you reject the null hypothesis, using a probability of Type I error x = 0.05, if the sample standard deviation from process 1 is 32 and from process 2 is
34?
SEVILTIMI provv/
(Round to three decimal places as needed.)
Transcribed Image Text:You have been asked to determine if two different production processes have different mean numbers of units produced per hour. Process 1 has a mean defined as μ₁ and process 2 has a mean defined as µ₂. The null and alternative hypotheses are H₂: μ₁ −μ₂ ≤0 and H₁ : µ₁ − µ₂ > 0. The process variances are unknown but assumed to be equal. Using random samples of 36 observations from process 1 and 49 observations from process 2, the sample means are 60 and 50 for populations 1 and 2 respectively. Complete parts a through d below. Click the icon to view a table of critical values for the Student's t-distribution. THIV IVVI VIMUVUV IVA Since the test statistic is IV The test statistic is t = MITM IV ܝ The critical value(s) is(are) 1.663. (Round to three decimal places as needed. Use a comma to separate answers as needed.) greater than t + ny – 2,0 ² reject Ho. c. Can you reject the null hypothesis, using a probability of Type I error x = 0.05, if the sample standard deviation from process 1 is 32 and from process 2 is 34? SEVILTIMI provv/ (Round to three decimal places as needed.)
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Follow-up Question
You have been asked to determine if two different production processes have different mean numbers of units produced
per hour. Process 1 has a mean defined as µ₁ and process 2 has a mean defined as µ₂. The null and alternative
hypotheses are Ho: H₁ H₂ ≤0 and H₁: μ₁ −μ₂ > 0. The process variances are unknown but assumed to be equal.
Using random samples of 36 observations from process 1 and 49 observations from process 2, the sample means are
60 and 50 for populations 1 and 2 respectively. Complete parts a through d below.
Click the icon to view a table of critical values for the Student's t-distribution.
The test statistic is t = 1.806. (Round to three decimal places as needed.)
The critical value(s) is(are) 1.663.
(Round to three decimal places as needed. Use a comma to separate answers as needed.)
reject Ho.
Since the test statistic is
greater than
The test statistic is t =
tnx + My-
-2,α¹
b. Can you reject the null hypothesis, using a probability of Type I error x = 0.05, if the sample standard deviation from
process 1 is 21 and from process 2 is 30?
(Round to three decimal places as needed.)
Transcribed Image Text:You have been asked to determine if two different production processes have different mean numbers of units produced per hour. Process 1 has a mean defined as µ₁ and process 2 has a mean defined as µ₂. The null and alternative hypotheses are Ho: H₁ H₂ ≤0 and H₁: μ₁ −μ₂ > 0. The process variances are unknown but assumed to be equal. Using random samples of 36 observations from process 1 and 49 observations from process 2, the sample means are 60 and 50 for populations 1 and 2 respectively. Complete parts a through d below. Click the icon to view a table of critical values for the Student's t-distribution. The test statistic is t = 1.806. (Round to three decimal places as needed.) The critical value(s) is(are) 1.663. (Round to three decimal places as needed. Use a comma to separate answers as needed.) reject Ho. Since the test statistic is greater than The test statistic is t = tnx + My- -2,α¹ b. Can you reject the null hypothesis, using a probability of Type I error x = 0.05, if the sample standard deviation from process 1 is 21 and from process 2 is 30? (Round to three decimal places as needed.)
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