Question

For each situation, perform a hypothesis test for the population mean. Be sure to show the null hypothesis H0 (with correct parameter), the alternative hypothesis H1, the P-level you get from ZTest, TTest, or 1-PropZTest (depending on whether you’re testing for µ or p, and whether σ is known or unknown), the result of the test (i.e. reject / do not reject H0) and the conclusion (interpret the result in English).

Studies suggest that 10% of the world’s population is left-handed. A researcher believes that mathematicians have a higher rate of left-handedness than the general population. He polls 85 mathematicians at random and finds that 12 of them are left-handed. Is this adequate evidence at the α = 0.05 level that mathematicians are more likely to be left-handed?

H0:

H1:

P-level:

Result:

Conclusion:

Answer 1

(1)

H0: Null Hypothesis: P = 0.10

(2)

HA: Alternativ Hypothesis: 0.10

(3)

P = Population proportion = 0.1

Q = 1 - P =0.9

n = Sample size = 85

p = Sample proportion = 12/85 =0.1412

SE =

=

Test staistic is:

Z= (0.1412 - 0.1)/0.0325 =1.2677

Table of Area Under Standard Normal Curve gives area = 0.3980

So,

P-Value = (0.5 - 0.3980) X 2 = 0.2040

(4)

Since P-Value is greater than = 0.05:

Result:

The difference is not sigifiacent. Fail to reject null hypothesis.

(5)

Conclusion: There is no adequate evidence at the = 0.05 level that mathematicians are more likely to be left - handed.