Final answer:
The question is about conducting a z-test for a population mean where the null hypothesis is the population mean equals 1190 (H0: μ = 1190), and the alternative hypothesis is the population mean is greater than 1190 (Ha: μ > 1190). It is a right-tailed test at a significance level of 0.07 with given sample statistics and a known population standard deviation.
Step-by-step explanation:
The question revolves around performing a hypothesis test for a population mean μ using a z-test at a significance level of α = 0.07.
The sample statistics provided include a sample mean (μ) of 1216.05, a population standard deviation (σ) of 195.97, and a sample size (n) of 250. The claim being tested is that the population mean is greater than 1190 (μ > 1190).
To set up the hypothesis test, the null hypothesis (H0) is that the population mean is equal to 1190 (H0: μ = 1190), and the alternative hypothesis (Ha) is that the population mean is greater than 1190 (Ha: μ > 1190).
This is a right-tailed test because the alternative hypothesis is looking for a mean greater than the null hypothesis value.
Steps to conduct the z-test using technology:
- Use a statistical software or calculator capable of performing a z-test. You want to access the function that allows input for hypothesis testing.
- Enter the null hypothesis value (μ0 = 1190), the population standard deviation (σ = 195.97), the sample mean (μ = 1216.05), and the sample size (n = 250).
- Set the alternative hypothesis to reflect the claim, which in this case is μ > 1190.
- Run the z-test calculation which will provide the z-score and the p-value.
- Interpret the results. If the p-value is less than the significance level (α = 0.07), reject the null hypothesis in favor of the alternative hypothesis. Conversely, if the p-value is greater, do not reject the null hypothesis.