A student pursuing a degree in English as a second language believes the proportion female factory workerswho can't speak English is less than the proportion of male factory workers who can't speak English. To testher claim she randomly selects 313 female factory workers and out of them 48 could not speak English. Shethen randomly selects 400 male factory workers and out of them 43 could not speak English. Test her claimat a=0.05 to see if she was right. The correct hypotheses are:O Ho:PF < PMНА: Pr > Рм (сclaim)O Ho:PF 2 PMHA:PF < PM(claim)O Ho:PF = pMHA:PF + PM(claim)Since the level of significance is 0.10 the critical value is -1.282The test statistic is:(round to 3 places)The p-value is:(round to 3 places)The decision can be made to:O reject HoO do not reject HoThe final conclusion is that:O There is enough evidence to reject the claim that the proportion female factory workers who can'tspeak English is less than the proportion of male factory workers who can't speak English.O There is not enough evidence to reject the claim that the proportion female factory workers whocan't speak English is less than the proportion of male factory workers who can't speak English.O There is enough evidence to support the claim that the proportion female factory workers who can'tspeak English is less than the proportion of male factory workers who can't speak English.O There is not enough evidence to support the claim that the proportion female factory workers whocan't speak English is less than the proportion of male factory workers who can't speak English.

Name: A student pursuing a degree in English as a second language believes
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Description: A student pursuing a degree in English as a second language believes the proportion female factory workerswho can't speak English is less than the proportion of male factory workers who can't speak English. To testher claim she randomly selects 313

Answered: A student pursuing a degree in English…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A student pursuing a degree in English as a second language believes the proportion female factory workers
who can't speak English is less than the proportion of male factory workers who can't speak English. To test
her claim she randomly selects 313 female factory workers and out of them 48 could not speak English. She
then randomly selects 400 male factory workers and out of them 43 could not speak English. Test her claim
at a=0.05 to see if she was right. The correct hypotheses are:
O Ho:PF < PM
НА: Pr > Рм (сclaim)
O Ho:PF 2 PM
HA:PF < PM(claim)
O Ho:PF = pM
HA:PF + PM(claim)
Since the level of significance is 0.10 the critical value is -1.282
The test statistic is:
(round to 3 places)
The p-value is:
(round to 3 places)
The decision can be made to:
O reject Ho
O do not reject Ho
The final conclusion is that:
O There is enough evidence to reject the claim that the proportion female factory workers who can't
speak English is less than the proportion of male factory workers who can't speak English.
O There is not enough evidence to reject the claim that the proportion female factory workers who
can't speak English is less than the proportion of male factory workers who can't speak English.
O There is enough evidence to support the claim that the proportion female factory workers who can't
speak English is less than the proportion of male factory workers who can't speak English.
O There is not enough evidence to support the claim that the proportion female factory workers who
can't speak English is less than the proportion of male factory workers who can't speak English.

Expert Solution

Step 1

Given Information:

Female:

Sample size (n) = 313

Number of female factory workers who could not speak English X = 48

Sample proportion is given by the formula:

$\hat{p} = \frac{X}{n} = \frac{48}{313} =$ 0.1533546 $\approx$ 0.1534

Male:

Sample size (n) = 400

Number of male factory workers who could not speak English X = 43

Sample proportion is given by the formula:

$\hat{p} = \frac{X}{n} = \frac{43}{400} =$ 0.1075

Claim: The proportion of female factory workers who can't speak English is less than the proportion male factory workers who can't speak English.

Formulate the Hypothesis as follows:

Null Hypothesis: $H_{o} : p_{F} \geq p_{M}$ i.e., proportion of female factory workers who can't speak English is greater than or equal to the proportion male factory workers who can't speak English.

Alternative Hypothesis: $H_{A} : p_{F} < p_{M}$ i.e., proportion of female factory workers who can't speak English is less than the proportion male factory workers who can't speak English.

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