1)Please Help In testing whether the means of two normal populations are equal, summary statistics computed for two independent samples are as follows: Assume that the population variances are equal. Then, the Pooled Variance is equal to: A) 0.1017
B) 1.2713
C) 0.3189
D) 1.1250
2-. Two samples of sizes 25 and 35 are independently drawn from two normal populations, where the unknown population variances are assumed to be equal. The number of degrees of freedom of the equal-variances t test statistic is: A) 60
B) 59
C) 35
D) 58
Degrees of freedom for this type of t-test is this:
df = n1 + n2 - 2
To solve these questions, we need to understand the concepts of pooled variance and the degrees of freedom for the equal-variances t test statistic. Let's break down the steps to find the answers.
1) Pooled Variance:
To find the pooled variance, we need to calculate the variance for each sample and then combine them using a formula. The formula for pooled variance is:
Pooled Variance = ((n1-1) * s1^2 + (n2-1) * s2^2) / (n1 + n2 - 2)
Where:
- n1 and n2 are the sample sizes for the two independent samples.
- s1^2 and s2^2 are the variances for the two independent samples.
From the question, we are given the summary statistics for the two independent samples, assuming equal population variances. However, we don't have the sample sizes or the variances. Without this information, we cannot calculate the pooled variance.
2) Degrees of Freedom for Equal-Variances t Test Statistic:
To find the degrees of freedom for the equal-variances t test statistic, we use the formula:
Degrees of Freedom = n1 + n2 - 2
Where:
- n1 and n2 are the sample sizes of the two independent samples.
From the question, we are given the sample sizes for the two samples: 25 and 35. We can plug these values into the formula to find the answer:
Degrees of Freedom = 25 + 35 - 2
Degrees of Freedom = 60
Therefore, the answer to question 2 is A) 60.
To summarize:
1) The Pooled Variance cannot be determined without the sample sizes and variances.
2) The number of degrees of freedom for the equal-variances t test statistic is 60.