We conclude that the percentage of employed workers who have registered to vote exceeds the percentage of unemployed workers who have registered to vote.

Step-by-step explanation:

We are given that 513 employed persons and 604 unemployed persons are independently and randomly selected, and that 287 of the employed persons and 280 of the unemployed persons have registered to vote.

Let $p_1$ = percentage of employed workers who have registered to vote.

$p_2$ = percentage of unemployed workers who have registered to vote.

So, Null Hypothesis, $H_0$ : $p_1\leq p_2$ {means that the percentage of employed workers who have registered to vote does not exceeds the percentage of unemployed workers who have registered to vote}

Alternate Hypothesis, $H_A$ : $p_1>p_2$ {means that the percentage of employed workers who have registered to vote exceeds the percentage of unemployed workers who have registered to vote}

The test statistics that would be used here Two-sample z test for proportions;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of employed workers who have registered to vote = $\frac{287}{513}$ = 0.56

$\hat p_2$ = sample proportion of unemployed workers who have registered to vote = $\frac{280}{604}$ = 0.46

$n_1$ = sample of employed persons = 513

$n_2$ = sample of unemployed persons = 604

So, the test statistics = $\frac{(0.56-0.46)-(0)}{\sqrt{\frac{0.56(1-0.56)}{513}+\frac{0.46(1-0.46)}{604} } }$

= 3.349

The value of z test statistics is 3.349.

Now, at 0.05 significance level the z table gives critical value of 1.645 for right-tailed test.

Since our test statistic is more than the critical value of z as 3.349 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the percentage of employed workers who have registered to vote exceeds the percentage of unemployed workers who have registered to vote.

5 0

2 years ago

How do I find the area of the shaded region? Thanks!!

bazaltina [42]

Answer:

The radius of a circumcircle of an equilateral triangle is equal to (a / √3), where ‘a’ is the length of the side of equilateral triangle.

Circle Radius = 16 / sq root (3)

Circle Radius = 9.237604307

Circle Area = PI * radius ^ 2

Circle Area = PI * 85.3333333333

Circle Area = 268.083

Equilateral Triangle area = side^2 * sq root (3) / 4

Equilateral Triangle area = 16^2 * 0.4330127019

Equilateral Triangle area = 110.85

Shaded region = 268.083 - 110.85

Shaded region = 157.233

Step-by-step explanation:

7 0

2 years ago

You were planning to spend $12 on a

nordsb [41]

You have $12, and need at least x more dollars to spend $30 total. So the inequality is 12 + x ≥ 30, where x is the number of dollars needed to get free delivery. To solve for x, subtract 12 from each side of the sign. x ≥ 30 - 12, x ≥ 18. You must spend at least 18 more dollars to qualify for free delivery.

8 0

1 year ago