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Tju [1.3M]
3 years ago
6

Last year, 50% of MNM, Inc. employees were female. It is believed that there has been a reduction in the percentage of females i

n the company. This year, in a random sample of 400 employees, 180 were female.
Based on this information, you want to determine if there has been a decrease in the percentage of females in the company (at the significance level of 5%). Round your solutions for this Exhibit to 4 decimal places.
Mathematics
1 answer:
anygoal [31]3 years ago
4 0

Answer:

We conclude that there has been a decrease in the percentage of females in the company from last year.

Step-by-step explanation:

We are given that Last year, 50% of MNM, Inc. employees were female. It is believed that there has been a reduction in the percentage of females in the company.

This year, in a random sample of 400 employees, 180 were female.

<u><em /></u>

<u><em>Let p = percentage of females in the company this year.</em></u>

So, Null Hypothesis, H_0 : p \geq 50%   {means that there has not been a decrease in the percentage of females in the company from last year}

Alternate Hypothesis, H_A : p < 50%   {means that there has been a decrease in the percentage of females in the company from last year}

The test statistics that will be used here is <u>One-sample z proportion</u> <u>statistics</u>;

                                   T.S.  = \frac{\hat p-p}{{\sqrt{\frac{\hat p(1-\hat p)}{n} } } } }  ~ N(0,1)

where, \hat p = proportion of female in a sample of 400 employees = \frac{180}{400} = 0.45

           n = sample of employees = 400

So, <u><em>test statistics</em></u>  =  \frac{0.45-0.50}{{\sqrt{\frac{0.45(1-0.45)}{400} } } } }

                               =  -2.0101

The value of the test statistics is -2.0101.

Now at 5% significance level, the z table gives critical value of -1.6449 for left-tailed test. Since our test statistics is less than the critical value of z as -2.0101 < -1.6449, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <u>we reject our null hypothesis</u>.

Therefore, we conclude that there has been a decrease in the percentage of females in the company from last year.

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