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MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is μ = 19 inches. However, a survey reported that of a random sample of 46 fish caught, the mean length was x = 18.6 inches, with estimated standard deviation s = 3.4 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than μ = 19 inches? Use α = 0.05.

 

What is the value of the sample test statistic? (Round your answer to three decimal places.)


Estimate the P-value.

a) P-value > 0.250
b) 0.100 < P-value < 0.250    
c) 0.050 < P-value < 0.100
d)0.010 < P-value < 0.050
e) P-value < 0.010
 
Sketch the sampling distribution and show the area corresponding to the P-value.
 
Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
a) At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
b) At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.    
c) At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
d) At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
 
Interpret your conclusion in the context of the application.
a) There is sufficient evidence at the 0.05 level to conclude that the average fish length is less than 19 inches.
b) There is insufficient evidence at the 0.05 level to conclude that the average fish length is less than 19 inches.  
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Expert Solution
Step 1

State the hypotheses.

Statistics homework question answer, step 1, image 1

That is, there is no evidence to conclude that average length of a trout caught in Pyramid Lake is less than 19 inches.

Statistics homework question answer, step 1, image 2

That is, there is evidence to conclude that average length of a trout caught in Pyramid Lake is less than 19 inches.

Decision rule:

Statistics homework question answer, step 1, image 3

Obtain the value of the test statistic.

The value of the test statistic is obtained below:

Statistics homework question answer, step 1, image 4

Thus, the value of the test statistic is –0.80.

Step 2

Obtain the degree of freedom:

Statistics homework question answer, step 2, image 1

Obtain the P-value.

The P-value is obtained below:

Use EXCEL Procedure for finding the P-value.

Follow the instruction to obtain the P-value:

  1. Open EXCEL
  2. Go to Formula bar.
  3. In formula bar enter the function as“=TDIST”
  4. Enter the test statistic value as ABS(–0.80).
  5. Enter the degrees of freedom as 45.
  6. Click enter.

EXCEL output:

From the EXCEL output, the P-value is 0.2140.

That is, the P-value lies between 0.100 and 0.250.

Correct option: Option b.

 

 

Step 3

 

Use EXCEL MEGASTAT to sketch the sampling distribution and show the area corresponding to the P-value.

EXCEL MEGASTAT procedure:

Step 1: In EXCEL, Select Add-Ins>MegaStat>Probability.

Step 2: Choose Continuous probability distributions.

Step 3: Select t-distribution and select calculate probability given t and enter t as –0.80.

Step 4: Enter df as 45.

Step 5: Click Ok.

EXCEL MEGASTAT output:

Statistics homework question answer, step 3, image 1

Correct option: option 1

 

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