How do I do this? I am very lost.
If you live in California, the decision to buy earthquake insurance is an important one. A survey revealed that only 133 of 337 randomly selected residences in one California county were protected by earthquake insurance. Calculate the appropriate test statistic to test the hypotheses that at least 40% buy the insurance.
Null hypothesis:
Ho: p = or > .40 -->meaning: population proportion is equal to or greater than .40
Alternative hypothesis:
Ha: p < .40 -->meaning: population proportion is less than .40
Using a formula for a binomial proportion one-sample z-test with your data included, we have:
z = .39 - .40 -->test value (133/337 = .39) minus population value (.40)
divided by √[(.40)(.60)/337]
Note: .60 = 1 - .40
I'll let you finish the calculation.
Hint: Null will not be rejected. You can draw your conclusion from there.
In a recent survey, 70% of the community favored building a haelth center in their neighborhood. If 14 citizens are chosen, find the probabilty that exactl 6 of them favore the building of the health center.
On your TI-84 Calculator Press "2nd" "VARS" for the [Distr] menu. Scroll down to binompdf( and press enter
Then enter in this order
binompdf(14,0.70,6) = 0.023
To calculate the appropriate test statistic for this hypothesis test, you can follow these steps:
Step 1: State the null and alternative hypotheses
- Null hypothesis (H0): The proportion of residences buying earthquake insurance is less than or equal to 40%
- Alternative hypothesis (Ha): The proportion of residences buying earthquake insurance is greater than 40%
Step 2: Calculate the test statistic (z-score)
- The test statistic in this case will be a z-score since we are dealing with proportions.
- The formula for calculating the z-score is:
z = (p - P) / sqrt((P * (1 - P)) / n)
- Where:
- p = sample proportion (133/337 = approximately 0.3949)
- P = hypothesized population proportion (0.40)
- n = sample size (337)
Step 3: Calculate the critical value
- Determine the significance level (α) for the test. Let's assume α = 0.05 (5% significance level).
- If the calculated z-score is greater than the critical value for the chosen significance level, we reject the null hypothesis.
Step 4: Compare the test statistic and critical value
- Look up the critical value corresponding to the chosen significance level from the z-table.
- If the test statistic is greater than the critical value, it means the result is statistically significant, and we reject the null hypothesis. If not, we fail to reject the null hypothesis.
Step 5: Interpret the results
- If the null hypothesis is rejected, it suggests that there is evidence to support the alternative hypothesis. In this case, it would mean that more than 40% of residences buy earthquake insurance.
Keep in mind that you will need access to a statistical software such as Excel, SPSS, or Python, to calculate the test statistic and interpret the results accurately.