An advertisement for a popular weight-loss clinic suggests that participants in its new diet program lose, on average, more than 10 pounds. A consumer activist decides to test the authenticity of the claim. She follows the progress of 29 women who recently joined the weight-reduction program. She calculates the mean weight loss of these participants as 10.8 pounds with a standard deviation of 1.6 pounds. The test statistic for this hypothesis would be __________.Multiple Choice−3.023.02−2.69
Question
An advertisement for a popular weight-loss clinic suggests that participants in its new diet program lose, on average, more than 10 pounds. A consumer activist decides to test the authenticity of the claim. She follows the progress of 29 women who recently joined the weight-reduction program. She calculates the mean weight loss of these participants as 10.8 pounds with a standard deviation of 1.6 pounds. The test statistic for this hypothesis would be __________.Multiple Choice−3.023.02−2.69
Solution
To calculate the test statistic for this hypothesis, we first need to state the null and alternative hypotheses.
The null hypothesis (H0) is that the mean weight loss is 10 pounds (the claim made by the weight-loss clinic). The alternative hypothesis (H1) is that the mean weight loss is more than 10 pounds.
The test statistic can be calculated using the formula:
Z = (X̄ - μ) / (σ / √n)
where:
- X̄ is the sample mean (10.8 pounds)
- μ is the population mean (10 pounds, according to the null hypothesis)
- σ is the standard deviation (1.6 pounds)
- n is the sample size (29 women)
Substituting the given values into the formula, we get:
Z = (10.8 - 10) / (1.6 / √29)
This simplifies to:
Z = 0.8 / (1.6 / √29)
Calculating the above expression will give us the Z-score or test statistic.
Please note that the exact value of the test statistic will depend on the precise value of √29, which is approximately 5.385.
So, the test statistic is not exactly -3.02, 3.02, or -2.69. You would need to calculate the exact value using the formula provided.
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