Two samples of the starting annual salaries (in thousands of dollars) of females

Question

Two samples of the starting annual salaries (in thousands of dollars) of females and males . a certain industry were collected. The sample of starting salaries of females yielded 5, ?? = 43.9, and 81 = 5.4. The sample of starting salaries of males yielded n,-7, i-428, and 82--27. Let ?? and ?2 denote the true mean salaries of the two populations (female and male starting salaries). (a) Find the estimated value of ??-12 and the estimated standard error. (b) Construct a 98% confidence interval for ??-742. (c) If you wish to use the collected data to determine whether there is evidence that starting salaries for females are on average higher than starting salaries for males, state the null and alternative hypotheses that you would use (d) To use the statistical procedures used in parts (a) and (b) above, what important assumption are you making? nswers:

Explanation / Answer

a) mu1 - mu2 = 43.9 - 42.8 = 1.1
estimated std.error = sqrt(s1^2/n1 +s2^2/n2)
= sqrt(5.4^2/5 + 2.7^2/7)
= 2.6217

b)
t value at 98% = 2.7638

CI = (x1 -x2) +/- t * sqrt(s1^2/n1 + s2^2/n2)
= (43.9 - 42.8) +/- 2.7638 *sqrt(5.4^2/5 + 2.7^2/7)
= (-6.1459 ,8.3459)

The 98% CI is (-6.1459 ,8.3459)

c)
H0 : mu1 = mu2
Ha : mu1 > mu2

t = (x1 -x2) / sqrt(s1^2/n1 +s2^2/n2)
= (43.9 - 42.8)/sqrt(5.4^2/5 + 2.7^2/7)
= 0.4196

P value = .3418

We can not reject the null hypothesis there is not sufficient evidence to support the claim

d) Assumptions are as:
1) The two populations have the same variance.
2) The populations are normally distributed.
3) Each value is sampled independently from each other value.

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