test the hypothesis that the average height of a male in USA is greater than 5'10 and the average height of a female is less than 5'6 at a 90 percent confidence level
Ho: male mean = 70"
Ha: male mean > 70"
Ho: female mean = 66"
Ha: female mean < 66"
What are your sample values to test these hypotheses? Sample means, standard deviations and number of scores?
To test these hypotheses, you would typically perform a hypothesis test using a sample of male and female heights in the USA. Here's a step-by-step guide on how to conduct the hypothesis test:
Step 1: Formulate the Null and Alternative Hypotheses
- Null Hypothesis (H0) for males: The average height of males in the USA is less than or equal to 5'10.
- Alternative Hypothesis (H1) for males: The average height of males in the USA is greater than 5'10.
- Null Hypothesis (H0) for females: The average height of females in the USA is greater than or equal to 5'6.
- Alternative Hypothesis (H1) for females: The average height of females in the USA is less than 5'6.
Step 2: Collect Data
- Randomly select a sample of male and female heights from the USA population.
Step 3: Calculate Descriptive Statistics
- Calculate the sample mean and sample standard deviation for both male and female heights.
Step 4: Conduct the Hypothesis Test
- Select an appropriate test statistic for the test (e.g., t-test or z-test). The choice depends on the sample size and whether the population standard deviation is known.
- Determine the level of significance (α) for the test (90% confidence level corresponds to α = 0.10).
For the male hypothesis:
- Calculate the t-score/z-score using the sample mean, sample standard deviation, population mean (5'10), and sample size.
- Determine the rejection region based on the test statistic and the chosen level of significance.
- Compare the test statistic with the critical value(s) to decide whether to reject or fail to reject the null hypothesis.
For the female hypothesis:
- Follow the same steps as above, but comparing the sample mean, sample standard deviation, population mean (5'6), and sample size.
Step 5: Draw Conclusions
- If the test statistic falls within the rejection region, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.
Remember that the specific calculations and test statistics used may vary depending on the nature of the data, the sample size, and the assumptions made. It is always recommended to consult statistical software or a statistician to ensure the most appropriate analysis for your specific situation.