A researcher suggests that male nurses earn more money than female nurses. A survey of 16 male and 20 female nurses reported the data below. Is there enough evidence, at Alpha = .01, to support the...

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Answer To: A researcher suggests that male nurses earn more money than female nurses. A survey of 16 male and...

David answered on Dec 20 2021
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Stat Assignment 8A
1) A researcher suggests that male nurses earn more money than female nurses. A
survey of 16 male and 20 female nurses reported the data below. Is
there enough evidence,
at Alpha = .01, to support the claim that male nurses earn more money?
Data is missing.
2) A company reported that an insured woman’s average stay in the hospital for normal
childbirth is 2.3 days, while an uninsured woman’s average stay is 1.9 days. Both samples
were of 16 women and the standard deviation for each was 0.6. At Alpha = .01, test the
claim that the means are equal. Then calculate the 99% confidence interval for the
difference of the means.
Solution:
Null Hypothesis (Ho): µ1 = µ2
Alternative Hypothesis (Ha): µ1 ≠ µ2
Pooled standard deviation, Sp = √ (n1 – 1) s1² + (n2 – 1) s²/ (n1 + n2 – 2)
= √ (15 x 0.6² + 15 x 0.6²)/ (16 + 16 – 2)
= 0.6
Test Statistics
t = (X-bar1 – X-bar2)/ Sp √1/n1 + 1/n2
= (2.3 – 1.9)/ 0.6 √1/16 + 1/16
= 1.89
Degrees of freedom, df = n1 + n2 – 2 = 16 + 16 – 2 = 30
Using t-tables, the critical value is
t (0.01/2, 30) = ±2.75
Since test statistics lie within the critical value, we fail to reject the null hypothesis.
There is sufficient evidence to conclude that the means are equal.
99% confidence interval is given by:-
(X-bar1 – X-bar2) ± t (α/2, df) Sp √1/n1 + 1/n2
(2.3 – 1.9) ± 2.75 x 0.6 √1/16 + 1/16
0.4 ± 0.58
-0.18, 0.98
Stat Assignment 8B
1) A basketball coach claims that by taking a “special” vitamin, a weight lifter can
increase his strength. Eight players are selected and given a test of strength. After two...
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