Question

A diet center claims that it has the most effective weight loss program in the region. Its advertisement says, "Participants in our program really lose weight." Five clients of this program are weighed on the first day of the diet and then three months later.

Client	Weight on First Day of Diet	Weight Three Months Later
1	151	147
2	201	195
3	152	151
4	190	185
5	190	192

a. Specify the null and alternative hypotheses to test whether the median difference for weight loss supports the diet center’s claim.

• H₀: m_D = 0; H_A: m_D ≠ 0

• H₀: m_D ≤ 0; H_A: m_D > 0

• H₀: m_D ≥ 0; H_A: m_D < 0

b. Calculate the value of the test statistic T. (Round your answer to 1 decimal place.)

Test Statistic_______

c. The p-value for the test is found to be equal to 0.064. At the 5% significance level, do the data support the diet center’s claim?

• Yes, since we reject H₀.

• Yes, since we do not reject H₀.

• No, since we reject H₀.

• No, since we do not reject H₀.

Answer 1

a. Since we want to see whether the diet actually affects weight loss or not.Our Null hypothesis = mean difference is 0 and alternative hypothesis is that = mean difference less than zero

b. We will be using paired t-test as we are testing the same sample again after some time. Using Shapiro - Wilks test we find the data to be normally distributed

The test statistic value is

statistic=1.9140405956690572, pvalue=0.12814794871344753

c. No, since we do not reject