1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Viktor [21]
2 years ago
13

A nutritionist has developed a diet that she claims will help people lose weight. Twelve people were randomly selected to try th

e diet. Their weights were recorded prior to beginning the diet and again after 6 months. Here are the original weights, in pounds, with the weight after 6 months in parentheses. Before 192 212 171 215 180 207 165 168 190 184 200 196 After 183 196 174 211 160 191 162 175 190 179 189 195 Test the claim that the diet is effective at the 0.05 level of significance.
Mathematics
1 answer:
deff fn [24]2 years ago
8 0

The diet which is developed by the nutritionist is effective at the 0.05 level of significance. Claim is agreed.

<h3>When do we use two-sample t-test?</h3>

The two-sample t-test is used to determine if two population means are equal.

A nutritionist has developed a diet that she claims will help people lose weight. In this,

  • Twelve people were randomly selected to try the diet.
  • Their weights were recorded prior to beginning the diet and again after 6 months.

Here are the original weights, in pounds, with the weight after 6 months in parentheses.

  • Before 192 212 171 215 180 207 165 168 190 184 200 196
  • After    183 196  174 211 160 191   162 175 190  179  189 195

The mean of the weights before 6 moths is,

\overline X_1=\dfrac{192+ 212 +171 +215 +180 +207 +165 +168 +190 +184 +200 +196 }{12}\\\overline X_1=190

The mean of the weights after 6 months is,

\overline X_2=\dfrac{ 183 +196  +174 +211 +160 +191   +162 +175 +190  +179  +189 +195  }{12}\\\overline X_1=183.75

Standard deviation of both the data is 16.9 and 14.7.

1. Null and Alternative Hypotheses.

The following null and alternative hypotheses need to be tested:

\begin{array}{ccl} H_0: \mu_1 & = & \mu_2 \\\\ \\\\ H_a: \mu_1 & > & \mu_2 \end{array}

This corresponds to a right-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used.

  • (2) Rejection Region

Based on the information provided, the significance level is α=0.05 and the degrees of freedom are df = 22. In fact, the degrees of freedom are computed as follows, assuming that the population variances are equal:

df_{Total} = df_1 + df_2 = 11 + 11 = 22

Hence, it is found that the critical value for this right-tailed test is

t_c=1.717, for α=0.05 and df=22

The rejection region for this right-tailed test is,

R = \{t: t > 1.717\}

(3) Test Statistics

Since it is assumed that the population variances are equal, the t-statistic is computed as follows:

t = \displaystyle \frac{\bar X_1 - \bar X_2}{\sqrt{ \frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2}(\frac{1}{n_1}+\frac{1}{n_2}) } }

\displaystyle \frac{ 190 - 183.75}{\sqrt{ \frac{(12-1)16.9^2 + (12-1)14.7^2}{ 12+12-2}(\frac{1}{ 12}+\frac{1}{ 12}) } } = 0.967

  • (4) Decision about the null hypothesis

Since it is observed that t=0.967≤tc=1.717 it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p=0.1721 and since p=0.1721≥0.05p = 0.1721  it is concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis H₀ is not rejected. Therefore, there is not enough evidence to claim that the population mean μ1​ is greater than μ2​, at the α=0.05 significance level.

Confidence Interval

The 95% confidence interval is −7.16<μ<19.66

Thus, the diet which is developed by the nutritionist is effective at the 0.05 level of significance. Claim is agreed.

Learn more about the two-sample t-test here;

brainly.com/question/27198724

#SPJ1

You might be interested in
What is the measure of Angle R?
Ivanshal [37]

The sum of angles in triangle is equal to 180 degrees, so

<R =180-56-30

<R=94

8 0
3 years ago
Read 2 more answers
Delia put I two bags of blocks in the left-side pan of a balance. Each bag has the
UkoKoshka [18]
I agree the top of me is correct :)
6 0
3 years ago
Enter the decimal equivalent of 11/8
lorasvet [3.4K]

Answer:

1.375

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
1. Name a pair of adjacent angles. Explain why they are adjacent.
AlekseyPX
1. Adjacent means they are next to each other and share equal common side and vertex. So its angleRUS and angleSUT.
2. If you see that little square that equals to 90 degrees so it’s the same thing as the adjacent
3. and M should be the line between V and T
3 0
3 years ago
I know its easy but i suck at math pls help
e-lub [12.9K]

Answer:

-6.8125

Step-by-step explanation:

Convert 13/16 to a decimal.

Write -6 down

You get -6.8125.

Hope this helps! If it does, please mark me brainliest, and press thank you to help me. Thank you! ;)

Good luck on whatever you are doing.

3 0
3 years ago
Read 2 more answers
Other questions:
  • There are two 5th grade classes at Jones Elementary School. Mrs. Roberts has 17 girls and 18 boys in her class. Mr. Simpson has
    8·2 answers
  • The distance formula is based on which theorem?
    6·2 answers
  • A chef plans to mix 100% vinegar with Italian dressing. The Italian dressing contains 12%
    8·1 answer
  • Henry is saving money to buy a game. so far he has saved $12 , which is three-fourths of the total cost of the game. how much do
    8·2 answers
  • Please help me on how to solve this question, it is really confusing, pleaseeeee
    15·1 answer
  • It takes 1 and 1 4th cups of milk to make 8 pancakes, how many cups of milk is needed to make 20
    11·1 answer
  • A florist sells 3 dozen bunches of flowers for $78. whites the cost per flower?
    13·1 answer
  • What else would need to be congruent to show that abc = xyz by asa
    12·2 answers
  • Daniel earns a commission of 3% on every home he sells. Recently, Daniel
    8·1 answer
  • Josh travels frequently. For a particular airline, it takes 20 minutes for the first bag to arrive in baggage claim after a flig
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!