Question
In: Statistics and Probability
The caloric contents and the sodium contents (in milligrams) of 10 beef hot dogs is given...
- The caloric contents and the sodium contents (in milligrams) of 10 beef hot dogs is given below. (Source: Consumer Reports)
|
Calories x |
150 |
170 |
120 |
120 |
90 |
180 |
170 |
140 |
90 |
110 |
|
Sodium y |
420 |
470 |
350 |
360 |
270 |
550 |
530 |
460 |
380 |
330 |
- Find the equation of the regression line.
Y = 80.819 +2.4715x
- Slope of the regression line you wrote in part A = 2.4715 Write a sentence to interpret this value in the context of the problem
- Calculate the correlation coefficient, r. Write a sentence to interpret this value in the context of the problem r = ______
Correlation of r is 0.9064
- Calculate the coefficient of determination, . Interpret this value in the context of the problem.
______ 0.
Calculated r^2 = 0.822
- Use the regression equation (in part A) to predict the value of sodium content (in milligrams) for a beef hot dog that has 130 calories.
- Using , conduct a t - test for significance to determine if there is a significant relationship between the caloric content and the sodium content of beef hot dogs.
Solutions
Expert Solution
Ru regression analysis in excel
Regression equation: y = 2.4715x + 80.813
Slope of the regression line you wrote in part A = 2.4715
Calculate the correlation coefficient, r. = 0.9064
Calculate the coefficient of determination, .= 0.822
formula =0.9062^2 = 0.822
Use the regression equation (in part A) to predict the value of sodium content (in milligrams) for a beef hot dog that has 130 calories.
x = 130
y = 2.4715x + 80.813
y = 2.4715*130+ 80.813
y = 402 (rounded to whole number)
so the predicted value of 130 calories is 402
Using , conduct a t - test for significance to determine if there is a significant relationship between the caloric content and the sodium content of beef hot dogs.
Run t-Test: Two-Sample Assuming Equal Variances in excel
P-value = 0.00000003 lesser than the significance level 0.05
The p-value less than 0.05 (typically ≤ 0.05) is statistically significant. It indicates strong evidence against the null hypothesis, as there is less than a 5% probability the null is correct . so there is a significant relationship between the caloric content and the sodium content of beef hot dogs
orchestra answered 3 years agoRelated Solutions
The caloric contents and the sodium contents (in milligrams) of 10 beef hot dogs is given...
The caloric contents and the sodium contents (in milligrams) of
10 beef hot dogs is given below. (Source: Consumer
Reports)
Calories
x
150
170
120
120
90
180
170
140
90
110
Sodium y
420
470
350
360
270
550
530
460
380
330
State the null and alternative
hypotheses in symbols and words
H0 =
Ha =
Calculate the t test
statistic. t = _______ Calculate the p-value. _________
Circle the correct
conclusion: Reject H0
or
...
The caloric contents and the sodium contents (in milligrams) of 10 beef hot dogs is given...
The caloric contents and the sodium contents (in milligrams) of
10 beef hot dogs is given below. (Source: Consumer
Reports)
Calories
x
150
170
120
120
90
180
170
140
90
110
Sodium y
420
470
350
360
270
550
530
460
380
330
State the null and alternative
hypotheses in symbols and words
H0 =
Ha =
Calculate the t test
statistic. t = _______ Calculate the p-value. _________
Circle the correct
conclusion: Reject H0
or
...
The chart below shows the caloric content and the sodium content(in milligrams) for 10 beef hot...
The chart below shows the caloric content and the sodium
content(in milligrams) for
10 beef hot dogs (Source: Consumer Reports).
Calories,x 150 170 120 120 90 180 170 140 90 110
Sodium, y 420 470 350 360 270 550 530 460 380 330
(a) Graph a scatter diagram of the table and nd the equation of
the regression
equation and plot it on the same scatter diagram to see the
regression line.
(b) What is the correlation coefficient(r) of the...
The chart below shows the caloric content and the sodium content(in milligrams) for 10 beef hot...
The chart below shows the caloric content and the sodium
content(in milligrams) for
10 beef hot dogs (Source: Consumer Reports).
Calories,x 150 170 120 120 90 180 170 140 90 110
Sodium, y 420 470 350 360 270 550 530 460 380 330
(a) Graph a scatter diagram of the table and nd the equation of
the regression
equation and plot it on the same scatter diagram to see the
regression line.
(b) What is the correlation coefficient(r) of the...
Fat contents (in percentage) for 10 randomly selected hot dogs were given in the article "Sensory...
Fat contents (in percentage) for 10 randomly selected hot dogs
were given in the article "Sensory and Mechanical Assessment of the
Quality of Frankfurters". Use the following data to construct a 90%
confidence interval for the true mean fat percentage of hot dogs:
(Give the answers to two decimal places.)
( , )
26.0
22.1
23.6
17.0
30.6
21.8
26.3
16.0
20.9
19.5
A nutrition laboratory tests 40 “reduced sodium” hot dogs, finding that the mean sodium content is...
A nutrition laboratory tests 40 “reduced sodium” hot dogs,
finding that the mean sodium content is 310 mg with a standard
deviation of 36 mg. Find a 95% confidence interval for the mean
sodium content of this brand of hot dog. Be sure to check all
necessary assumptions and conditions, and interpret your interval
within the context of the problem.
Conduct a hypothesis test at the .025 level as to whether the
mean sodium content level is 300mg. Provide
H0,Ha,...
A nutrition laboratory tests 50 "reduced sodium" hot dogs, finding that the mean sodium content is...
A nutrition laboratory tests 50 "reduced sodium" hot dogs,
finding that the mean sodium content is 307 mg, with a standard
deviation of 37 mg.
a) Find a 95% confidence interval for the mean sodium content
of this brand of hot dog.
b) What assumptions have you made in this inference? Are the
appropriate conditions satisfied?
c) Explain clearly what your interval means.
A nutrition laboratory tests 60 "reduced sodium" hot dogs, finding that the mean sodium content is...
A nutrition laboratory tests 60 "reduced sodium" hot dogs,
finding that the mean sodium content is 305 mg, with a standard
deviation of 35 mg.
a) Find a 95% confidence interval for the mean sodium content
of this brand of hot dog
. b) What assumptions have you made in this inference? Are the
appropriate conditions satisfied?
c) Explain clearly what your interval means.
A researcher would like to predict the calories in a beef hot dog from the sodium...
A researcher would like to predict the calories in a beef hot
dog from the sodium content of the hot dog. She gathers a sample of
20 hot dogs, and calculates the following summary statistics
• The average sodium content is 401.15mg.
• The average calorie count is 156.85cal.
• The standard deviation in sodium content is 102.43mg.
• The standard deviation in calorie count is 22.64cal.
• The predicted increase in calorie count when sodium content
increases by 1mg...
The accompanying data are the caloric contents and the sugar contents (in grams) of 11 high-fiber...
The accompanying data are the caloric contents and the sugar
contents (in grams) of 11 high-fiber breakfast cereals. What is
the equation of the regression line? Use the regression equation to
predict the value of y for each of the given x-values.
a) x=150 b)x=90 c)x=175 d)x=198
Calories (x): 140 190 170 170 170 180 190 200 190 160 160
Sugar (y): 6 9 6 9 10 16 13 18 20 10 10
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