Question Help study compared waight loss between patients on diet A and patients
ID: 3323168 • Letter: Q
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Question Help study compared waight loss between patients on diet A and patients omplete parts (a) through (d) State the null and altemative et 1 represent the mean number of pounds patients on diet A lose in six months and on diet B. Patients on diet A lost a mean of 7.9 pounds in six months, whereas patients on diet B lost a mean of 7.4 pounds in s On a sample of 500 paints on det A and 500 patio ts ond et B adhestandard deviati nofthe amont Ost 3.6 po ds for det A and apo tr hypotheses if you want to test whether the mean t weight loss between the two diets is equal. What are the null and atemative hypotheses? 2 represente mean number of pounds patients on det B lose in six nents Choose te oret anseer beo. In the context of this study, what is the meaning of a Type I error? A. A Type I error is commited when one concdludes that there is not a significant difference in mean wesight loss between the two diets when there a significant B. A Type I error is commited when one concludes that there is a significant dilference in mean weight los between the two diets when thare is not a significant Giference C. A Type I error is committed when one rejects both the null and altemative hypotheses D. A Type 1 error is commited when the null hypothesis is rejected when there is a significant difference in the mean weight loss between the two diets In the context of this study, what is the meaning of a Type Il error? A. A Type Il error is oommitted when one concludes that there is not a B. A Type ll error is committed when one concludes that there is not a C. A Type lt error is committed when one condludes that there is a significant dilference in mean weight loss between the two diets when there is not a significant difference difference in mean weight loss between the two diets when there is indeed a significant difference difference in mean weight loss of only diet A ck to select your answer(s).Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: 1 - 2 = 0
Alternative hypothesis: 1 - 2 0
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample z-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), z statistic test statistic (z).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 0.2154
z = [ (x1 - x2) - d ] / SE
z = 2.32
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between the population means, and SE is the standard error.
Since we have a two-tailed test, the P-value is the probability that a z statistic is more extreme than - 2.32; that is, less than - 2.32 or greater than 2.32.
Thus, the P-value = 0.0204
Interpret results. Since the P-value (0.0204) is less than the significance level (0.05), we cannot accept the null hypothesis.
Reject H0, There is evidence of differnce in the mean weight loss of patients between the two diets.
Type I error is commited when one concludes the significant difference in mean weight between two diets when there is not a significant difference.
Type II error is commited when one concludes that there is not significant difference in mean weight between two diets when indeed there is a significant difference.
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