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 2 pounds within a month." Six clients of this program are weighed on the first day (Before) of the diet and then one month later (After). A portion of the data is shown in the accompanying table. (You may find it useful to reference the appropriate table: z table or t table) Client Before After 1 163 161 2 204 196 : : : 6 153 136 Let the difference be defined as Before - After. a. Specify the null and alternative hypotheses that test the diet center's claim. H0: ?D = 2; HA: ?D ? 2 H0: ?D ? 2; HA: ?D < 2 H0: ?D ? 2; HA: ?D > 2 b. Assuming that weight loss is normally distributed, calculate the value of the test statistic. (Round final answer to 2 decimal places.) Test statistic c. Find the p-value. 0.05 < p-value < 0.10 0.01 < p-value < 0.025 0.025 < p-value < 0.05 p-value < 0.01 p-value > 0.10 d. At the 10% significance level, do the data support the diet center's claim? No since the p-value is less than ?. Yes since the p-value is more than ?. No since the p-value is more than ?. Yes since the p-value is less than ?.
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To calculate the weight loss for each client, subtract the weight after one month (After) from the weight before starting the program (Before). Client 1: 161 - 163 = -2 pounds Client 2: 196 - 284 = -88 pounds Client 3: 6 - 2 = 4 pounds Client 4: 136 - 153 = -17 Show more…
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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?
David N.
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 one 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. Weight on First Day of Diet: 158, 199, 186, 201, 166, 148 Weight One Month Later: 161, 196, 189, 178, 162, 136 Let the difference be defined as Before - After. a. Specify the null and alternative hypotheses that test the diet center's claim: Ho: μD = 3; HA: μD ≠3 Ho: μD ≥ 3; HA: μD < 3 Ho: 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 (select interval): 0.050 < p-value < 0.100 0.005 < p-value < 0.010 p-value > 0.200 0.010 < p-value < 0.025 0.025 < p-value < 0.050 d. At the 5% significance level, do the data support the diet center's claim?
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