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3 years ago

Can someone please help ASAP!

Mathematics

1 answer:

Zolol [24]3 years ago

7 0

Pick’s Theorem is used to find the areas of figures on lattices easily. The formula is:

A = (B)/2 + I - 1, where B is the number of points on the border of the shape, and I is the number of points inside the shape.

Here, there are 8 points on the outside of the shape, and there are 12 points inside the shape. So, we do:

8/2 + 12 - 1 = 4 + 12 - 1 = 15 units squared.

We can check by finding the areas of the non-shaded region and subtracting that area from the whole rectangle area of 4 * 10 = 40:

4 * 1 + (3 * 1)/2 + 1 * 9 + (3 * 1)/2 + (9 * 2)/2 = 25

40 - 25 = 15, so we’re right!

The answer is 15 units squared, or choice (B).

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(a) Null Hypothesis, $H_0$ : p = 0.50

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(c) The sampling distribution of the sample statistic is Normal distribution.

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Step-by-step explanation:

We are given that a 0.1 significance level is used for a hypothesis test of the claim that when parents use a particular method of gender selection, the proportion of baby girls is greater than 0.5.

Assume that sample data consists of 78 girls in 144 births.

Let p = population proportion of baby girls

(a) So, Null Hypothesis, $H_0$ : p = 0.50 {means that the proportion of baby girls is equal to 0.50}

Alternate Hypothesis, $H_A$ : p > 0.50 {means that the proportion of baby girls is greater than 0.50}

(b) The value of level of significance (α) given in the question is 0.10.

(c) The sampling distribution of the sample statistic is Normal distribution.

(d) This test is right-tailed as in the alternative hypothesis we are concerned for proportion of baby girls that is greater than 0.50.

(e) The test statistics that would be used here One-sample z test for proportions;

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

where, $\hat p$ = sample proportion of baby girls = $\frac{78}{144}$ = 0.54

n = sample of births = 144

So, the test statistics = $\frac{0.54-0.50}{\sqrt{\frac{0.54(1-0.54)}{144} } }$

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The value of z test statistics is 0.96.

(f) The P-value of the test statistics is given by;

P-value = P(Z > 0.96) = 1 - P(Z < 0.96)

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Therefore, we conclude that the proportion of baby girls is equal to 0.50.

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