i need help setting up a math question.. statistics?
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The makers of a dietary supplement claim their product will help ppl lose weight. the company obtains a random sample of 950 adult males aged 20 to 74 who take the supplement and finds their mean weight loss after eight weeks to be 0.9 pounds. assume the population standard deviation weight loss is 7.2 pounds. A) state the null and alternative hypotheses. i dont know what the numbers here would be.. can anyone help. thanks.
The null hypothesis is of the form “no change / no difference”. Your alternative is that there is a significant difference at a given level (usually 0.95 or 0.99).
The basic question is whether a difference in mean of 0.9 is significant with a sample size of 950 and sigma of 7.2. Calculate your Z score, look it up on the table, and see whether it’s significant.
Hypothesis Test for mean:
assuming you have a large enough sample such that the central limit theorem holds and the mean is normally distributed then to test the null hypothesis H0: μ = Δ
find the test statistic z = (xBar – Δ) / (sx / sqrt(n))
where xbar is the sample average
sx is the sample standard deviation
n is the sample size
The p-value of the test is the area under the normal curve that is in agreement with the alternate hypothesis.
H1: μ > Δ; p-value is the area to the right of z
H1: μ < Δ; p-value is the area to the left of z
H1: μ ≠ Δ; p-value is the area in the tails greater than |z|
In your question you have the null and alternative hypotheses:
H0: μ ≤ 0 vs H1: μ > 0
where μ is the mean weight loss.
the test statistic is z = (0.9 – 0) / (7.2 / sqrt(950))
z = 3.852759
the p-value for the test is equals
P( Z > 3.852759) = 0.00005839717
with such a small p-value we reject the null hypothesis and conclude the alternate is true and the mean weight loss is greater than zero.