Question

Asked Jun 17, 2019

2 views

Natasha is a physician looking to determine whether a supplement is effective in helping men lose weight. She takes a random sample of overweight men and records their weights before the trial. Natasha then prescribes the supplement and instructs them to take it for four weeks while making no other lifestyle changes. After the four-week period, she records the weights of the men again. Suppose that the data were collected for a random sample of 6 men, where each difference is calculated by subtracting the weight before the trial from the weight after the trial. Assume that the populations are normally distributed. The test statistic is t≈−2.795, α=0.05, the corresponding rejection region is t<−2.015, the null hypothesis is H0:μd=0, and the alternative hypothesis is Ha:μd<0.

Which of the following statements are accurate for this hypothesis test in order to evaluate the claim that the true mean difference between the weight of men after the trial and the weight before the trial is less than zero?

A) Reject the null hypothesis that the true mean difference between the weight of men after the trial and the weight before the trial is equal to zero.

B) Fail to reject the null hypothesis that the true mean difference between the weight of men after the trial and the weight before the trial is equal to zero.

C) Based on the results of the hypothesis test, there is enough evidence at the α=0.05 level of significance to suggest that the true mean difference between the weight of men after the trial and the weight before the trial is less than zero.

D) Based on the results of the hypothesis test, there is enough evidence at the α=0.05 level of significance to suggest that the true mean difference between the weight of men after the trial and the weight before the trial is greater than zero.

Step 1

**Test statistic results:**

For testing whether a supplement is effective in helping men lose weight or not, it is given to assume that the populations are normally distributed.

*Null and alternative hypotheses:*

Null hypothesis:

*H*_{0}: µ_{d} = 0

That is, the true mean difference between the weight of men after the trial and the weight before the trial is equal to zero.

Alternative hypothesis:

*H*_{a}: µ_{d} < 0

That is, the true mean difference between the weight of men after the trial and the weight before the trial is less than zero.

Significance level, *α* = 0.05.

*t*-statistic = −2.795

Rejection region, *t*_{crit} = −2.015

Step 2

**Decision Rule:**

If *t* > *t*crit, reject null hypothesis.

Here, *t-*statistic < *t*crit. Hence, we **fail to reject null hypothesis at 0.05 significance level**.

**Statement that is accurate for this hypothesis test:**

According to the given null hypothesis, the tr...

Tagged in

Find answers to questions asked by student like you

Show more Q&A

Q: Flying over the western states with mountainous terrain in a small aircraft is 40% riskier than flyi...

A: (a) Poisson distribution:It is a discrete probability distribution that models the number of events ...

Q: Jane has stored three albums on her iPod. The first album consists of 11 songs by Frank Sinatra, the...

A: In this question, there is total 32 songs collection out of which 11 songs by Frank Sinatra, 13 song...

Q: please answer the whole question (3) Let x be per capita income in thousands of dollars. Let y be t...

A: Hi, since the problem posted by you contains multiple sub-parts, we are answering the first three su...

Q: Given that z is a standard normal random variable, find z for each situation (to 2 decimals) a. The ...

A: a.The area to the left of z is 0.209 can be written as P(Z < z)=0.209.In the z-table for negative...

Q: Listed below are brain volumes, measured in cubic centimeters, of twins at birth. Use a 5% significa...

A: Solution:Null and alternative hypotheses:Null hypothesis: µ1 − µ2 = 0 (equivalently µ1 = µ2)Alternat...

Q: Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? ...

A: (a) Scatter diagram of the data:The line that best fits the data is least-squares regression line.Th...

Q: Q5. You are considering two investment choices: a. 1 year CD that pays 2% for sure; b. investing in ...

A: Portfolio Mean and SDI am answering all the sub-partsQ5. You are considering two investment choices:...

Q: Listed below are the amounts of mercury (in parts per million, or ppm) found in tuna sushi sample...

A: In this question, we have the data of amount of mercury in tuna sushi stores using the data we have ...

Q: Midterm exam scores are normally distributed with a mean of 75 and a standard deviation of 6. If the...

A: According to the question , Midterm exam scores are normally distributed with a mean of 75 and a sta...