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. Client Weight on First Day of Diet Weight One Month Later 1 169 162 2 244 239 3 175 174 4 201 184 5 161 156 6 147 141 Let the difference be defined as Before - After. a. Specify the null and alternative hypotheses that test the diet center's claim. H0: μD = 3; HA: μD ≠ 3 H0: μD ≥ 3; HA: μD < 3 H0: μD ≤ 3; HA: μD > 3 b. 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.) Test statistic: _____ c. Approximate the p-value. 0.100 < p-value < 0.200 0.005 < p-value < 0.010 0.050 < p-value < 0.100 0.010 < p-value < 0.025 0.025 < p-value < 0.050 d. 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.

Client   Weight on First Day of Diet   Weight One Month Later
1        169                          162
2        244                          239
3        175                          174
4        201                          184
5        161                          156
6        147                          141

Let the difference be defined as Before - After.

a. Specify the null and alternative hypotheses that test the diet center's claim.
H0: μD = 3; HA: μD ≠ 3
H0: μD ≥ 3; HA: μD < 3
H0: μD ≤ 3; HA: μD > 3

b. 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.)
Test statistic: _____

c. Approximate the p-value.
0.100 < p-value < 0.200
0.005 < p-value < 0.010
0.050 < p-value < 0.100
0.010 < p-value < 0.025
0.025 < p-value < 0.050

d. At the 1% significance level, do the data support the diet center's claim?

Added by Hunter T.

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