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 5% significance level, do the data support the diet center’s claim?

Client Weight on First
Day of Diet Weight One
Month Later 1 162 157 2 197 207 3 189 161 4 193 181 5 162 159 6 142 138 TABLE 2 Student's Distrib Entles n prortde the odned for TABLE 2 IContinuedo that to a given ber of deg of food For A76 .328 0.10 575 /571 2.770 2.080 2.074 037 2024 2.020 2008 005 2.000 2449 2429 2402 2400 239 239) 2345 2334 4604 4032 3707 3499 3106 2098 285 2019 2750 0.00 2.744 2.700 2,724 2.674 2.062

Explanation / Answer

a)

H0: D 3; HA: D < 3

b)

test statistics = 1.369

c)

0.050 < p-value < 0.100

d)

No since the p-value is more than .

Weight first day of diet Weight one month later Mean 174.167 167.167 Variance 485.367 567.367 Observations 6.000 6.000 Pearson Correlation 0.854 Hypothesized Mean Difference 0.000 df 5.000 t Stat 1.369 P(T<=t) one-tail 0.115 t Critical one-tail 2.015 P(T<=t) two-tail 0.229 t Critical two-tail 2.571

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