The null and alternate hypotheses are: H0 : μ1 = μ2 H1 : μ1 ≠ μ2 A random sample of 15 observations from the first population revealed a sample mean of 350 and a sample standard deviation of 12. A random sample of 17 observations from the second population revealed a sample mean of 342 and a sample standard deviation of 15. At the 0.10 significance level, is there a difference in the population means?

Step-by-step explanation:

From the information given,

The formula for determining the t test statistic is

t = (x1 - x2)/√(s1²/n1 + s2²/n2)

Where

x1 = sample mean of the first population

x2 = sample mean of the second population

s1 = sample standard deviation of the first population

s2 = sample standard deviation of the second population

n1 = number of samples in the first population

n2 = number of samples in the second population

From the information given,

x1 = 350

x2 = 342

s1 = 12

s2 = 15

n1 = 15

n2 = 17

Therefore,

t = (350 - 342)/√(12²/15 + 15²/17)

= 8/√(9.6 + 13.24)

= 1.674

degree of freedom is

n2 + n1 - 2 = 17 + 15 - 2 = 30

The test is 2 tailed. Using the test statistic calculator, the probability value is 0.105

Comparing the probability value with the significance level, there is no significant difference. Therefore, we would fail to reject the null hypothesis

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