test the claim that μ1 = μ2 Two samples are randomly selected from normal populations. The sample statistics are
n1=11,x(bar)=4.8, s1=.76
n2=18, x(bar)=5.2, s2=.51
Assume that σ1 ≠ σ2
Use alpha = .02
I am not sure if this is a 2-sample t test or do I use ANOVA?
Please show me all steps to get to the answer.
Alpha = .02
Am I using the 2-sample T test or ANOVA?
Calculate Z = (μ1-μ2)/Standard Error (SE) for difference between means.
SE Difference = sq. rt. of (SE1^2 + SE2^2)
SE = Standard Deviation/Sq rt of n-1
Since it is two-tailed, look for Z < .01 to reject null hypothesis.
I hope this helps. Thanks for asking.
To test the claim that μ1 = μ2, where μ1 and μ2 are the population means of two normal populations, you can use a two-sample t-test.
Here are the steps to perform the test:
Step 1: State the null and alternative hypotheses
The null hypothesis (H0) states that the population means are equal: μ1 = μ2
The alternative hypothesis (Ha) states that the population means are not equal: μ1 ≠ μ2
Step 2: Determine the significance level (alpha)
The significance level, denoted as α, is the probability of rejecting the null hypothesis when it is true. In this case, alpha is given as α = 0.02.
Step 3: Calculate the test statistic
The test statistic for a two-sample t-test is given by:
t = (x1 - x2) / sqrt((s1^2 / n1) + (s2^2 / n2))
where:
x1 and x2 are the sample means
s1 and s2 are the sample standard deviations
n1 and n2 are the sample sizes
Using the given sample statistics, we have:
x1 = 4.8, x2 = 5.2, s1 = 0.76, s2 = 0.51, n1 = 11, and n2 = 18
t = (4.8 - 5.2) / sqrt((0.76^2 / 11) + (0.51^2 / 18))
Step 4: Determine the critical value(s)
The critical value(s) are obtained from the t-distribution table, considering the degrees of freedom (df). For a two-sample t-test, the degrees of freedom can be approximated using the smaller of the two sample sizes minus one.
In this case, choose the smaller value between n1 - 1 and n2 - 1.
df = min(n1 - 1, n2 - 1)
Step 5: Determine the rejection region(s)
To determine the rejection region, compare the absolute value of the test statistic with the critical value(s) obtained in Step 4. Reject the null hypothesis if the absolute value of the test statistic is greater than the critical value(s).
Step 6: Calculate the p-value
The p-value is the probability of getting a test statistic at least as extreme as the observed, assuming the null hypothesis is true. The p-value can be calculated using software or by referencing the t-distribution table.
Step 7: Make a decision
Compare the p-value with the significance level (alpha) to make a decision. If the p-value is less than alpha, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.
Based on the given information, you can follow these steps to get the answer. Remember to use the appropriate t-distribution table or statistical software to find the critical value(s) and calculate the p-value.