Question

The following equation can "clearly" be simplified: In{ lim{f(x)-- - (X-1'] +$}} + (sinº q + cos?q) + (sinºq + cos?q) = Ë cosh pV I – tanhº p 2" n=0 A random sample of 70 statisticians indicated that 51 know how to simplify it. A second random sample (independent from the first) indicated that 42 of 500 mathemagicians know how to simplify it. Is the proportion of mathemagicians who know how to simplify the equation different from 7%? Using a 10% significance level, what is the appropriate conclusion? Select one: a. Since p-value > a, there is insufficient evidence that the proportion is equal to 5%. cross out b. Since p-value > a, there is insufficient evidence that the proportion is different from 5%. cross out c. Since p-value < a, there is sufficient evidence that the proportion is different from 5%. cross out d. Since p-value < a, there is insufficient evidence that the proportion is different from 5%. cross ou e. Since p-value > a, there is sufficient evidence that the proportion is different from 5%. cross out

Answer 1

Answer: Since p-value > $\boldsymbol{\alpha}$ there is insufficient evidence that the proportion is different from 7%

Explanation:

Null Hypothesis, Ho: The proportion of Mathematicians who can solve the equation is 0.07

i.e.P 0.07

Alternative Hypothesis, Ho=a: The proportion of Mathematicians who can solve the equation is significantly different from 0.07

$\boldsymbol{i.e. P \neq 0.07}$

Test-Statistics: Under Ho,

  
р Z = P P*(1-P) 2 N(0, 1) n

  $\boldsymbol{\hat{p} =\frac{42}{500}=0.084}$

Therefore,

  $\boldsymbol{Z = \frac{0.084-0.07}{\sqrt{\frac{0.07*0.93}{500}}} = 1.227}$

$\boldsymbol{P-value = P[|Z| > 1.227] = 0.2198}$