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. a. What are the null and the alternative hypotheses?b. At 95% confidence using the critical value approach, determine if there has been a significant reduction in the proportion of females.

We conclude that there has been a significant reduction in the proportion of females.

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 400

p = 50% = 0.5

Alpha, α = 0.05

Number of women, x = 118

First, we design the null and the alternate hypothesis  

This is a one-tailed test.  

Formula:

Putting the values, we get,

Now, we calculate the critical value.

Now,

Since the calculated z-statistic is less than the critical value, we fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.

Thus, there has been a significant reduction in the proportion of females.

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.