Question 7: Weight loss: In a study to determine whether counseling could help people lose weight, a sample of people experienced a group-based behavioral intervention, which involved weekly meetings with a trained interventionist for a period of six months. The following data are the numbers of pounds lost for 14 people. Assume the population is approximately normal. Perform a hypothesis test to determine whether the mean weight loss is greater than 13 pounds. Use the a=0.05  level of significance and the P-value method with the TI-84 Plus calculator. 21.2 27.5 6.5 22.8 20 11.5 16.2 19.7 36.3 32.5 11.1 34.8 22.4 17.9   Part 1: (a) State the appropriate null and alternate hypotheses. H0: (BLANK) H1:(BLANK) This hypothesis test is a (BLANK) tests. Answer Choice: Left-Tailed Right-Tailed Two-Tailed   Part 2: (b) Compute the value of the test statistic. Round the answer to at least three decimal places. t = (BLANK)     Part 3: (c) Compute the P-value. Round the answer to at least four decimal places. P-value: (BLANK)     Part 4: (d) Determine whether to reject H0. (BLANK) the null hypothesis H0   Answer Choice: Reject Do Not Reject   Part 5: (e) State a conclusion. There (BLANK) is enough evidence to conclude that the mean weight loss is greater than 13 pounds.   Answer Choice: Is Is Not

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...