A group of researchers are interested in the possible effects of distracting stimuli during eating, such as an increase or decrease in the amount of food consumption. To test this hypothesis, they monitored food intake for a group of 44 patients who were randomized into two equal groups. The treatment group ate lunch while playing solitaire, and the control group ate lunch without any added distractions. Patients in the treatment group ate an average of 52.1 grams of biscuits, with a standard deviation of 45.1 grams, and patients in the control group ate an average of 27.1 grams of biscuits, with a standard deviation of 26.4 grams. Do these data provide convincing evidence that the average food intake (measured in grams of biscuits consumed) is different for the patients in the treatment group? Assume that conditions for inference are satisfied.

Using the t-distribution, it is found that since the p-value of the test is of 0.0302, which is less than the standard significance level of 0.05, the data provides convincing evidence that the average food intake is different for the patients in the treatment group.

At the null hypothesis, it is tested if the consumption is not different, that is, if the subtraction of the means is 0, hence:

[tex]H_0: \mu_1 - \mu_2 = 0[/tex]

At the alternative hypothesis, it is tested if the consumption is different, that is, if the subtraction of the means is not 0, hence:

[tex]H_1: \mu_1 - \mu_2 \neq 0[/tex]

Two groups of 22 patients, hence, the standard errors are:

[tex]s_1 = \frac{45.1}{\sqrt{22}} = 9.6154[/tex]

[tex]s_2 = \frac{26.4}{\sqrt{22}} = 5.6285[/tex]

The distribution of the differences is has:

[tex]\overline{x} = \mu_1 - \mu_2 = 52.1 - 27.1 = 25[/tex]

[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{9.6154^2 + 5.6285^2} = 11.14[/tex]

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.

Hence:

[tex]t = \frac{25 - 0}{11.14}[/tex]

[tex]t = 2.2438[/tex]

The p-value of the test is found using a two-tailed test, as we are testing if the mean is different of a value, with t = 2.2438 and 22 + 22 - 2 = 42 df.

Since the p-value of the test is of 0.0302, which is less than the standard significance level of 0.05, the data provides convincing evidence that the average food intake is different for the patients in the treatment group.

A similar problem is given at https://brainly.com/question/25600813

An item costs $300 before tax, and the sales tax is $9.90 . Find the sales tax rate. Write your answer as a percentage.

41 divided by 533 estimate it and its long division and I have to find the R

(3x-6)/(x^2+2) what is the answer

What is 2 and 2/3 x 5

When 21 is subtracted from the square of a number, the result is 4 times the number.
Find the positive solution.

Is the set (3,1),(6,4),(9,7),(12,10) a function? Explain how you know

Jayden’s rectangular garden is 5 3/4 feet long and 4 1/2 feet wide. What is the area, in square feet, of the garden

Stella is ordering a taxi from an online taxi service. The taxi charges $3 just for the pickup and then an additional $1.75 per mile driven.

PLS help me pls no links 15 points in total

Write seven million two thousand five hundred in standard form

What is the remainder when you divide 2x3 4x2 - x 3 by x 2?.

What is the mean absolute deviation of the data set? {12, 4, 30, 16, 18} 2. 8 5 2006. 4 16.

Solve for x. Round to the nearest tenth of a degree, if necessary.

Yuri surveyed a random sample of 75 students in his school about their favorite color. Of the students surveyed, 49 chose lavender as their favorite color. If there are 908 students at the school, what is a valid estimate of the number of students whose favorite color is lavender?

600 students

300 students

450 students

800 students

which one?

Solve for x with 10x+10 and 17x+8

942 flowers in157 vases= flowers per vase

i’ll give you brainliest, thank you sm

9 is multiplied by the cube of a number.

y=2x-7
y=3x
can someone help solve for x and y

A number b subtracted from seven is greater than eight. What is the sentence as an inequality?

I need help with finding the slope.

Can y’all figure this out while I help my fam hang up a chrismus tree :)

I don’t understand please help

find the mode of the following set data

3, 10, 36, 26, 19, 2, 2, 40

I WILL GIVE 30 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT

You estimate the weight of an apple to be 6 ounces. The actual weight of an apple is 4 ounces. What is your percent error?




help

What is the sum of the first 12 terms in the series shown below?

1.5 - 4.5 + 13.5 - 10.5 +

angle x and angle y are complementary angles. angle x is eight times larger than angle y. what are the measurements of angle x and angle y?

Solve:
(a+b+c) (a+b-c)

Write a linear equation that describes the problem.