It is pretty common across most schools to find the grades at the MBA level divided between A's and B's. As such, you expect the mean GPA to be around 3.50. Using the sample of 200 MBA students, conduct a one-sample hypothesis test to determine if the mean GPA is different from 3.50. Use a .05 significance level.
2. Assume you read in the Whatsamatta U website that the average age of their MBA students is 45. Is this really true or have they failed to update this correctly? You think it is far less because there have been a lot more students going straight from their Bachelors to their Masters since the economy is so bad. You took a sample of 200 students (in the data file). Conduct a one-sample hypothesis test to determine if the mean age is less than 45. Use a .05 significance level.
3. You have heard from idle chatter that most students don't declare a major in their MBA programs. You took a sample of 200 students (in the data file). Conduct a one-sample hypothesis test to determine if the proportion without a major is greater than 50%. Use a .05 significance level.
Whatsamatta I question 2 need answer
2. One-Sample Hypothesis Test for Mean Age:
Null hypothesis: The mean age of MBA students is equal to 45 (μ = 45)
Alternative hypothesis: The mean age of MBA students is less than 45 (μ < 45)
Significance level (α) = 0.05
To conduct the one-sample hypothesis test for mean age, we will use the t-test.
Step 1: Set up the hypotheses:
H0: μ = 45
H1: μ < 45
Step 2: Select a significance level (α) = 0.05.
Step 3: Compute the test statistic:
We will use the t-test formula:
t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
Step 4: Determine the rejection region:
Since it is a one-tailed test with μ < 45, the rejection region is on the left side of the t-distribution curve.
Step 5: Calculate the p-value:
Using the t-distribution table or software, calculate the p-value associated with the test statistic.
Step 6: Decide whether to reject or fail to reject the null hypothesis:
Compare the p-value with the significance level.
- If the p-value < α, reject the null hypothesis.
- If the p-value ≥ α, fail to reject the null hypothesis.
Step 7: Interpret the results:
If the null hypothesis is rejected, it suggests that there is sufficient evidence to conclude that the average age of MBA students is less than 45.
3. One-Sample Hypothesis Test for Proportion without a Major:
Null hypothesis: The proportion of MBA students without a major is equal to 50% (p = 0.50)
Alternative hypothesis: The proportion of MBA students without a major is greater than 50% (p > 0.50)
Significance level (α) = 0.05
To conduct the one-sample hypothesis test for proportion, we will use the z-test.
Step 1: Set up the hypotheses:
H0: p = 0.50
H1: p > 0.50
Step 2: Select a significance level (α) = 0.05.
Step 3: Compute the test statistic:
We will use the z-test formula:
z = (sample proportion - population proportion) / sqrt((population proportion * (1 - population proportion)) / sample size)
Step 4: Determine the rejection region:
Since it is a one-tailed test with p > 0.50, the rejection region is on the right side of the z-distribution curve.
Step 5: Calculate the p-value:
Using the z-distribution table or software, calculate the p-value associated with the test statistic.
Step 6: Decide whether to reject or fail to reject the null hypothesis:
Compare the p-value with the significance level.
- If the p-value < α, reject the null hypothesis.
- If the p-value ≥ α, fail to reject the null hypothesis.
Step 7: Interpret the results:
If the null hypothesis is rejected, it suggests that there is sufficient evidence to conclude that the proportion of MBA students without a major is greater than 50%.
To conduct one-sample hypothesis tests for each of the given questions, you will need to follow these steps:
1. Define the Null Hypothesis (H0) and Alternate Hypothesis (H1):
- H0: The mean GPA/age/proportion is equal to the claimed value (3.50 for GPA, 45 for age, 50% for the proportion)
- H1: The mean GPA/age/proportion is different/less/greater than the claimed value
2. Determine the significance level (α):
- In this case, the significance level is given as 0.05
3. Collect and analyze data:
- For the mean GPA, you have a sample of 200 MBA students
- For mean age and proportion without a major, you also have a sample of 200 MBA students
4. Determine the test statistic based on the type of hypothesis test and data:
- For mean GPA and mean age, you can use the t-test since the population standard deviation is unknown
- For proportion without a major, you can use the z-test because you are testing a proportion
5. Calculate the test statistic and p-value:
- For mean GPA and mean age, you can use software or calculators to calculate the test statistic and p-value
- For proportion without a major, you can calculate the test statistic using the formula:
- z = (p̂ - p) / √((p * (1-p)) / n)
- p̂: sample proportion
- p: claimed proportion
- n: sample size
6. Determine the critical value(s) or rejection region:
- For a two-tailed test, you divide the significance level by 2, resulting in two critical values
- For a one-tailed test (less than or greater than), you find the critical value corresponding to the significance level
7. Make a decision:
- If the test statistic falls within the rejection region or if the p-value is less than the significance level, reject the null hypothesis
- If the test statistic does not fall within the rejection region or if the p-value is greater than the significance level, fail to reject the null hypothesis
8. State your conclusion:
- If you reject the null hypothesis, it means there is enough evidence to support the alternative hypothesis
- If you fail to reject the null hypothesis, it means there is not enough evidence to support the alternative hypothesis
Please note that for calculating the test statistic and p-value, you can use statistical software, calculators, or Excel functions.