a captain claims that at least 85% of the residents in his barangay have household pets. to test this claim a researcher randomly selected a sample of 550 residents and find that 495 of them do have household pets. at 0.05 level of significance.

formula that i used: z=p-P(population proportion/square root of p(p-1)/n

I DON'T KNOW WHAT TO DO.. please help. and is this one tailed test??

To determine whether the captain's claim is supported by the sample data, you can perform a statistical hypothesis test using the formula you mentioned. And yes, this is a one-tailed test.

Let's break down the process step by step:

Step 1: Define the Null Hypothesis and Alternative Hypothesis
The null hypothesis (H0) assumes that the captain's claim is true or that at least 85% of the residents have household pets. The alternative hypothesis (Ha) assumes that the captain's claim is not true or that less than 85% of the residents have household pets.
H0: p ≥ 0.85 (claim is true)
Ha: p < 0.85 (claim is not true)

Step 2: Determine the Level of Significance
In this case, the level of significance is given as 0.05, which means you are willing to accept a 5% chance of rejecting the null hypothesis even if it's true.

Step 3: Calculate the Test Statistic
The test statistic you will use is the z-test. The formula you mentioned is correct:
z = (p - P) / sqrt(P * (1 - P) / n)
where:
p represents the sample proportion (495/550 = 0.9),
P represents the hypothesized population proportion (0.85),
n represents the sample size (550).

Substituting these values into the formula, the calculation is as follows:
z = (0.9 - 0.85) / sqrt(0.85 * (1 - 0.85) / 550)

Step 4: Determine the Critical Value
Since this is a one-tailed test and we are testing if the proportion is less than 0.85, you'll need to find the critical value corresponding to a 0.05 level of significance. You can look up this critical value in the z-table or use a statistical software/tool.

Step 5: Compare the Test Statistic with the Critical Value
If the test statistic is smaller than the critical value, you will reject the null hypothesis. Otherwise, you'll fail to reject the null hypothesis.

Step 6: Draw a Conclusion
Based on the comparison between the test statistic and the critical value, you can make a conclusion. If the null hypothesis is rejected, then there's evidence to suggest that the claim made by the captain is not true. If the null hypothesis is not rejected, then there is not enough evidence to suggest that the claim is false.

I hope this helps! Let me know if you have any further questions.