90% of adults drink milk.
A sample of adults in an area was taken.
657 of 750 drink milk.
Do these responses provide strong evidence that the 90% figure is not accurate for this region?
I figured it out and got the P-value to be .028
How do I explain this?
With 750 persons and a 90% probability, the most probable result would be 0.9*750 = 675 and the standard deviation would be sqrt[0.9*0.1*750] = 8.2.
657 is 2.2 sigma less than the mean. That may be consistent with your P-value of 0.028, but I'm not certain what that means.
I do not consider that to be strong evidence that the 90% figure is not correct.
I checked a normal distribution table and found a probability of only 1.4% that the number of milk drinkers would be 657 or less. That does strongly suggest the fraction may be less than 90% for that region.
To explain the analysis and results obtained, you can use the following steps:
Step 1: Set up the hypotheses
The null hypothesis (H0) assumes that the proportion of adults who drink milk in the region is indeed 90%.
The alternative hypothesis (Ha) assumes that the proportion differs from 90%.
Step 2: Calculate the test statistic
For this situation, you will use a one-sample proportion z-test. Calculate the test statistic (z) using the formula:
z = (p̂ - P0) / √[P0(1 - P0) / n]
where:
- p̂ is the sample proportion who drink milk
- P0 is the hypothesized proportion (90% or 0.9 in decimal form)
- n is the sample size (750 in this case)
Step 3: Determine the p-value
Using the normal distribution, determine the area in the tail(s) of the distribution based on the test statistic (z-score). This will give you the p-value, which represents the probability of observing a sample proportion at least as extreme as the one obtained, assuming the null hypothesis is true.
Step 4: Compare the p-value to the significance level
Typically, a significance level (α) of 0.05 (or 5%) is used. If the obtained p-value is less than the significance level, we reject the null hypothesis - indicating strong evidence against the 90% figure.
In your case, you have obtained a p-value of 0.028. Since 0.028 is less than 0.05, we have strong evidence to reject the null hypothesis in favor of the alternative hypothesis. This suggests that the 90% figure is not accurate for this region, as the proportion of adults who drink milk likely differs from 90%.
Remember, the p-value represents the probability of obtaining a result as different from the null hypothesis as that observed, assuming the null hypothesis is true. A smaller p-value indicates stronger evidence against the null hypothesis.