A diet center claims that it has the most effective weight loss program in the r

Question

A diet center claims that it has the most effective weight loss program in the region. Its advertisements say, “Participants in our program lose more than 3 pounds within a month.” Six clients of this program are weighed on the first day of the diet and then one month later. Let the difference be defined as Weight on First Day of Diet minus Weight One Month Later. Use Table 2.

Specify the null and alternative hypotheses that test the diet center’s claim.

Assuming that weight loss is normally distributed, calculate the value of the test statistic. (Round all intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

At the 1% significance level, do the data support the diet center’s claim?

A diet center claims that it has the most effective weight loss program in the region. Its advertisements say, “Participants in our program lose more than 3 pounds within a month.” Six clients of this program are weighed on the first day of the diet and then one month later. Let the difference be defined as Weight on First Day of Diet minus Weight One Month Later. Use Table 2.

Explanation / Answer

b)

Test statistics:

Before After dbar

1 169 162 7

2 244 239 5

3 175 174 1

4 201 184 17

5 161 156 5

6 147 141 6

Mean 6.833333333

Before(1) After(2)

n 6 6

mean(?) 182.8333333 176

std. dev. 34.88504933 34.22864298

SE(s/sqrt(n)) 14.2418 13.9738

dbar = ?(before) - ?(after) = 6.833333333

s(dbar) = 5.3821

SE = s(dbar)/sqrt(n) = 2.1972

Test Statisitcs,

t = dbar - D/SE

= (6.8333 - 3) / 2.1972

= 1.74

c)

degrees of freedom = n-1 5

p-value = .0712

P value < 0.01

d)

No, because p value is greater than 0.01

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