In a 60 MA Economics students selected as sample are found to have a mean height of 68 inches and a
50 MBS students selected as sample have a mean height of 69 inches. Would you conclude that
management students are taller than economics students? Assume that standard derivation of height of
post graduate students to be 2.24 inches.
Z = (mean1 - mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√n
If only one SD is provided, you can use just that to determine SEdiff.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability
related to the Z score.
To determine if management students are taller than economics students, we can conduct a hypothesis test. Here's how you can do it step-by-step:
Step 1: State the Null Hypothesis (H0) and Alternative Hypothesis (H1):
H0: The mean height of management students is equal to or less than the mean height of economics students.
H1: The mean height of management students is greater than the mean height of economics students.
Step 2: Determine the significance level (α):
Let's assume a significance level of 0.05, which corresponds to a 95% confidence level.
Step 3: Collect the necessary information:
We have the following information:
- Sample size (n1) for economics students = 60
- Sample size (n2) for management students = 50
- Mean height (x1) for economics students = 68 inches
- Mean height (x2) for management students = 69 inches
- Standard deviation (σ) for postgraduate students = 2.24 inches
Step 4: Conduct the hypothesis test:
We can calculate the test statistic using the formula:
t = (x1 - x2) / sqrt((s1^2/n1) + (s2^2/n2))
Where:
s1 = standard deviation of economics students
s2 = standard deviation of management students
In this case, we will assume that the standard deviations of the populations (economics and management students) are the same or equal to 2.24 inches.
Step 5: Calculate the test statistic:
t = (68 - 69) / sqrt((2.24^2/60) + (2.24^2/50))
Step 6: Determine the critical value and the rejection region:
Since we are testing if management students are taller, and the alternative hypothesis is one-tailed, we will compare the t-value with the critical value from the t-distribution table.
For a significance level of 0.05 and degrees of freedom equal to the smaller sample size minus 1, in this case, 49:
The critical value for a one-tailed test is approximately 1.68.
Step 7: Make a decision:
If the calculated t-value is greater than the critical value, we reject the null hypothesis. This indicates that there is evidence that management students are taller than economics students. If the calculated t-value is less than the critical value, we fail to reject the null hypothesis.
Step 8: Calculate the t-value:
Substituting the values into the formula, we get:
t = (68 - 69) / sqrt((2.24^2/60) + (2.24^2/50))
Step 9: Compare the calculated t-value with the critical value:
If the calculated t-value is greater than the critical value of 1.68, then we can conclude that management students are taller than economics students.
Please substitute the values and calculate the test statistic to complete the analysis.
To determine if management students are taller than economics students, we need to perform a statistical analysis called a hypothesis test. In particular, we will conduct a two-sample t-test to compare the means of the two groups.
Here are the steps to conduct the hypothesis test:
Step 1: Set up the null hypothesis (H₀) and alternative hypothesis (H₁):
- H₀: There is no difference in the mean heights of management and economics students.
- H₁: Management students have a greater mean height than economics students.
Step 2: Determine the significance level (α), which is the probability of rejecting the null hypothesis when it is true. Let's assume a significance level of 0.05 (5%).
Step 3: Calculate the test statistic:
- The test statistic for a two-sample t-test is calculated as:
t = (mean₁ - mean₂) / sqrt[(var₁/n₁) + (var₂/n₂)]
where:
mean₁ and mean₂ are the sample means (68 and 69 inches, respectively),
var₁ and var₂ are the population variances (2.24^2 = 5.0176),
n₁ and n₂ are the sample sizes (60 and 50, respectively).
Step 4: Determine the critical value(s) or the p-value:
- The critical value is obtained from the t-distribution table or a statistical software. It depends on the degree of freedom and the significance level. With a sample size of 60+50-2=108 (degrees of freedom), the critical value is obtained as t-critical = 1.66 (approximated from the table).
- The p-value is the probability of obtaining a test statistic as extreme as the observed, assuming the null hypothesis is true. It can also be calculated using statistical software. If the p-value is less than the significance level (α), we reject the null hypothesis; otherwise, we fail to reject it.
Step 5: Compare the test statistic with the critical value or p-value:
- If the test statistic is greater than the critical value (t > t-critical), we reject the null hypothesis and conclude that management students are taller than economics students.
- If the p-value is less than the significance level (p < α), we reject the null hypothesis and conclude the same.
Remember, statistical significance does not imply practical significance. A statistically significant difference may not be practically meaningful.
Please note that the calculations involved in this test can be done using statistical software like R, Excel, or online statistical calculators.