Help? Elementary statistis Math 10s0 Problem 2. Are low-fat diets er low-carb di

Question

Help?

Elementary statistis Math 10s0 Problem 2. Are low-fat diets er low-carb diets more effective for weight loss? A sample or 70 subjects went on diet for At the end of time, the sample mean with a sample standard deviation of 7 pounds. A second sample of 76 subjects went on a low-fat diet. sample mean weight loss was 180 with a standard deviation of T26 Can you conclade that the mean weight loss differed between the two diets? Use the a 0.05 level. Ay type of Two problem Two means, independent populations, ei and or unknown and not assumed Two means inde known 3 Two means, independent and assumed equal Teo means from two dependent populations. 5.) Two proportions. 6) Two variances or standard deviatiom Bo write down the null and the allemative hypotheses Ho identify which is the claim. Identify: Left-, Right Two-tailed test: (Show the dif calculation if relevant, what is the formula for the Test Statistic? F) identify the values for all factors comprising the Test statistic. What are the test requirements? show they are satisfied, or identify any assumpions that must be made. what is the value of the Test statistic? What is your conclusion?

Explanation / Answer

Solution:-

Two means independent population, 1 and 2  unknown, but assumed equal.

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 t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = sqrt[(s12/n1) + (s22/n2)]

SE = 1.19

DF = 143.5

D.F= 144

t = [ (x1 - x2) - d ] / SE

t = - 6.30

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 t statistic having 144 degrees of freedom is more extreme than -6.30; that is, less than -6.30 or greater than 6.30.

Thus, the P-value = less than 0.0001

Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we have to accept the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that mean loss weight differed in two diets.

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.