It is claimed that participants of a popular weight loss programme have a mean weight loss of 10 pounds after 1 month. A medical researcher randomly selected 30 participants of the programme and recorded their weight loss (in pounds) after 1 month. The data was inputted into MINITAB for analysis. Exhibit 1, below, was subsequently generated. Exhibit 1 One-Sample Z: Weight Loss Test of mu = 10 vs < 10 The assumed standard deviation = 2.5 Variable N Mean StDev SE Mean Z P Weight Loss 30 8.977 2.463 ? * ** a) Calculate the missing value ‘?’. b) Construct the 97% confidence interval for the population mean weight loss for participants on this popular weight loss programme. c) State the null and the alternative hypotheses for this test. d) Determine the missing value ‘∗’. e) Use the tables provided to approximate the missing value ‘∗∗’. f) Using a level of significance α of 5%, state the decision and conclusion for this test.
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 + ...
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