Twenty students assigned to an experimental group receive 30 in a control group has a mean of 38 on the test (with an estimated population standard deviation of 3); the control group has a mean of 35 (with an estimated population standard deviation of 5). Using the .05 level, what should the experimenter conclude?
(a) use the steps of hypothesis testing
(b)sketch the distributors involved
(c)explain your answer to someone who is familar with the test for a single sample, but not independent means
I am confused on how to answer this question. Can somebody please help.
Im confused by your statement "Twenty students assigned to an experimental group receive 30 in a control group"
To answer this question, we need to follow the steps of hypothesis testing. Here's how you can approach it:
Step 1: State the hypotheses
The null hypothesis (H0) states that there is no significant difference between the means of the experimental and control groups. The alternative hypothesis (Ha) states that there is a significant difference between the means of the two groups.
Step 2: Set the significance level
In this case, the significance level is given as 0.05, which means we are willing to accept a 5% chance of making a Type I error (rejecting the null hypothesis when it is actually true).
Step 3: Calculate the test statistic
For testing independent means, we can use the two-sample t-test. The formula for the test statistic is:
t = (x1 - x2) / sqrt((s1^2/n1) + (s2^2/n2))
Where:
x1 and x2 are the means of the experimental and control groups, respectively,
s1 and s2 are the estimated population standard deviations of the two groups,
n1 and n2 are the sizes of the two groups.
In this case, x1 = 38, x2 = 35, s1 = 3, s2 = 5, n1 = 20, n2 = 30. By substituting these values into the formula, we can calculate the test statistic.
Step 4: Determine the critical value
The critical value is the value beyond which we reject the null hypothesis. To determine this value, we can look it up in the t-distribution table or use statistical software. With a significance level of 0.05 and degrees of freedom (df) = n1 + n2 - 2, we can find the critical value.
Step 5: Compare the test statistic with critical value
If the absolute value of the test statistic is greater than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Step 6: Make the conclusion
Based on the comparison in step 5, we can either conclude that there is a significant difference between the means of the experimental and control groups, or there is not enough evidence to support a significant difference.
To explain this to someone familiar with the test for a single sample but not independent means (c), you can compare it to a single sample t-test. In a single sample t-test, you compare the mean of a sample to a known population mean. In this case, we are comparing the means of two independent groups to see if they are significantly different from each other.
When conducting a hypothesis test for independent means, we follow similar steps as in a single sample test, but with additional calculations and considerations for the two groups. We calculate the test statistic using the means and standard deviations of both groups, and then compare the test statistic to a critical value to make a conclusion.
By following these steps and explaining the process, you will be able to answer the question and provide a clear explanation to someone who is familiar with a single sample test but not independent means.