Consider the test of hypothesis for the equality of two population means. The sample data from the first population is: n = 10, x-bar = 52.4, s = 5. The sample data from the second population is: n = 8, x-bar = 48.2, s = 6. Both variables are normally distributed and the population variances are assumed to be equal. The pooled estimate of the common population standard deviation is:
Question 15 options:
6.71
2.59
5.46
1.23
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To find the pooled estimate of the common population standard deviation, we can use the formula:
sp = sqrt(((n1-1)*(s1^2) + (n2-1)*(s2^2)) / (n1 + n2 - 2))
where sp is the pooled estimate of the common population standard deviation, n1 and n2 are the sample sizes of the first and second populations respectively, s1 and s2 are the sample standard deviations of the first and second populations respectively.
Given the sample data:
For the first population: n1 = 10, x̅1 = 52.4, s1 = 5
For the second population: n2 = 8, x̅2 = 48.2, s2 = 6
We can substitute these values into the formula:
sp = sqrt(((10-1)*(5^2) + (8-1)*(6^2)) / (10 + 8 - 2))
sp = sqrt(((9)*(25) + (7)*(36)) / (16))
sp = sqrt((225 + 252) / 16)
sp = sqrt(477 / 16)
sp ≈ sqrt(29.81)
sp ≈ 5.46
Therefore, the pooled estimate of the common population standard deviation is approximately 5.46. So, the correct answer is 5.46.