Question

1. In an experiment to determine the effect of ambient temperature on the emissions of oxides of nitrogen of diesel trucks, 10 trucks were run at temperatures of 40°F and 80°F. The emissions, in parts per billion, are presented in the following table. Truck 40°F 80°F 1 834.7 815.2 2 753.2 765.2 3 855.7 842.6 4 901.2 797.1 5 785.4 764.3 6 862.9 819.5 7 882.7 783.6 8 740.3 694.5 9 748.0 772.9 10 848.6 794.7 Paired t Hypothesis Test Summary Differences = $X_1 - X_2$ $\mu_d$: mean of population differences Null Hypothesis $H_0: \mu_d = 0$ Alternative Hypothesis $H_1: \mu_d > 0$ Mean of Sample Differences 36.31 T-Statistic 2.713015 P-Value 0.01194 df 9 Standard Error 13.383634 Can you conclude that the mean emissions are higher at 40°F? Use the provided SALT output for a Paired t Test and a significance level of 0.05. (a) State the hypothesis. (b) State the test statistic. (Round to 2 decimal places) (c) State the P-value. (Round to 4 decimal places) (d) What is your decision? (e) State a conclusion.

          1. In an experiment to determine the effect of ambient temperature on the emissions of oxides of nitrogen of diesel trucks, 10 trucks were run at temperatures of 40°F and 80°F. The emissions, in parts per billion, are presented in the following table.
Truck 40°F 80°F
1 834.7 815.2
2 753.2 765.2
3 855.7 842.6
4 901.2 797.1
5 785.4 764.3
6 862.9 819.5
7 882.7 783.6
8 740.3 694.5
9 748.0 772.9
10 848.6 794.7
Paired t Hypothesis Test Summary
Differences = $X_1 - X_2$
$\mu_d$: mean of population differences
Null Hypothesis $H_0: \mu_d = 0$
Alternative Hypothesis $H_1: \mu_d > 0$
Mean of Sample Differences 36.31
T-Statistic 2.713015
P-Value 0.01194
df 9
Standard Error 13.383634
Can you conclude that the mean emissions are higher at 40°F? Use the provided SALT output for a Paired t Test and a significance level of 0.05.
(a) State the hypothesis.
(b) State the test statistic. (Round to 2 decimal places)
(c) State the P-value. (Round to 4 decimal places)
(d) What is your decision?
(e) State a conclusion.

Show more…

1. In an experiment to determine the effect of ambient temperature on the emissions of oxides of nitrogen of diesel trucks, 10 trucks were run at temperatures of 40°F and 80°F. The emissions, in parts per billion, are presented in the following table.
Truck 40°F 80°F
1 834.7 815.2
2 753.2 765.2
3 855.7 842.6
4 901.2 797.1
5 785.4 764.3
6 862.9 819.5
7 882.7 783.6
8 740.3 694.5
9 748.0 772.9
10 848.6 794.7
Paired t Hypothesis Test Summary
Differences = X1 - X2
: mean of population differences
Null Hypothesis H0: = 0
Alternative Hypothesis H1: > 0
Mean of Sample Differences 36.31
T-Statistic 2.713015
P-Value 0.01194
df 9
Standard Error 13.383634
Can you conclude that the mean emissions are higher at 40°F? Use the provided SALT output for a Paired t Test and a significance level of 0.05.
(a) State the hypothesis.
(b) State the test statistic. (Round to 2 decimal places)
(c) State the P-value. (Round to 4 decimal places)
(d) What is your decision?
(e) State a conclusion.

Added by Ann R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Lucas Finney

12/12/2022

Step 1

The alternative hypothesis is that the mean emissions are higher at 40°F. Show more…

Show all steps

lock

Thanks for your feedback!

1. In an experiment to determine the effect of ambient temperature on the emissions of oxides of nitrogen of diesel trucks, 10 trucks were run at temperatures of 40°F and 80°F. The emissions, in parts per billion, are presented in the following table. Truck 40°F 80°F 1 834.7 815.2 Paired t Hypothesis Test Summary 2 753.2 765.2 Differences = X1 - X2 3 855.7 842.6 μα: mean of population differences 4 901.2 797.1 Null Hypothesis Ho: μα = 0 5 785.4 764.3 Alternative Hypothesis Η₁: μα > 0 6 862.9 819.5 Mean of Sample Differences 36.31 7 882.7 783.6 T-Statistic 2.713015 8 740.3 694.5 P-Value 0.01194 9 748.0 772.9 df 9 Standard Error 13.383634 10 848.6 794.7 Can you conclude that the mean emissions are higher at 40°F? Use the provided SALT output for a Paired t Test and a significance level of 0.05. (a) State the hypothesis. (b) State the test statistic. (Round to 2 decimal places) (c) State the P-value. (Round to 4 decimal places) (d) What is your decision? (e) State a conclusion.

Play audio

Feedback

Powered by NumerAI

Lucas Finney and 91 other subject Intro Stats / AP Statistics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

00:01 All right, so for this problem, we first want to figure out what our null and alternative hypotheses are.

00:07 The null hypothesis would be that the mean difference, mean diff, is equal to zero, that is population mean difference, and the alternative hypothesis based on the setup to the problem here, if the emissions are higher at 40 degrees fahrenheit, then if we're doing 40 minus 80, then the alternative hypothesis should be that the mean difference is greater than zero.

00:37 So what we want to do is first calculate out the difference for each one of our trucks.

00:44 So we do 834 .7 minus 815 .2 for a result of 19 .5, and then apply the same idea for each one of these.

00:54 Then for our little table of values for the difference, we can see that, well, there are 10, or the sample size is 10.

01:02 Using excel, which i'm assuming you are intended to do this problem in excel, based on the format of how everything was given here.

01:10 We can find the mean difference by taking the average over the difference column.

01:15 The s -d -d -e -v -s for sample standard deviation.

01:20 Grab everything in our difference column.

01:23 Then the standard error is going to be equal to the standard, or pardon me, the standard deviation of the differences, divided by the square root of the sample size.

01:35 So we divide by the square root of 10, getting a result of roughly 13 .4.

01:40 Then for the information down here, the number of degrees of freedom is going to be our sample size, n, minus 1.

01:50 So we have nine degrees of freedom.

01:53 Our test statistic, t, i'll write out the formula explicitly on screen here, one second...

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later