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 7 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. (You may find it useful to reference the appropriate table: z table or t table) Client Weight on First Day of Diet Weight One Month Later 1 161 155 2 216 207 3 173 175 4 197 182 5 162 154 6 150 135 Click here for the Excel Data File Let the difference be defined as Before – After. a. Specify the null and alternative hypotheses that test the diet center’s claim. H0: μD = 7; HA: μD ≠ 7 H0: μD ≥ 7; HA: μD < 7 H0: μD ≤ 7; HA: μD > 7 b. Assuming that weight loss is normally distributed, calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) c. Find the p-value. p-value <

0.01 0.05 p-value < 0.10 p-value 0.10 0.025 p-value < 0.05 0.01 p-value < 0.025 d. At the 5% significance level, do the data support the diet center’s claim? No since the p-value is less than α. Yes since the p-value is more than α. Yes since the p-value is less than α. No since the p-value is more than α. rev: 11_26_2019_QC_CS-192130 Next

Answer 1

= (6 + 9 + (-2) + 15 + 8 + 15)/6 = 8.5

s_d = sqrt(((6 - 8.5)^2 + (9 - 8.5)^2 + (-2 - 8.5)^2 + (15 - 8.5)^2 + (8 - 8.5)^2 + (15 - 8.5)^2)/5) = 6.3482

The test statistic is

  

c) P-value = P(T > 0.58)

                   = 1 - P(T < 0.58)

                   = 1 - 0.7065

                   = 0.2935

P-value > 0.10

No since the p-value is more than .