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solmaris [256]
3 years ago
12

Cullen is 10 years younger than Ada. The product of their ages 2 years ago was 39.

Mathematics
1 answer:
Klio2033 [76]3 years ago
8 0

Answer:

15

Step-by-step explanation:

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For a large supermarket chain in a particularâ state, aâ women's group claimed that female employees were passed over for manage
PolarNik [594]

Answer:

1) As the P-value (0.097) is greater than the significance level (0.05), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the women's claim that female employees were passed over for management training in favor of their male colleagues.

2) The 95% confidence interval for the population proportion is (0.173, 0.427).

The populations proportion (π=0.4) is included in this confidence interval, so the claim has no enough evidence to be supported.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that female employees were passed over for management training in favor of their male colleagues.

We use the women's part for sample and population proportions.

Then, the null and alternative hypothesis are:

H_0: \pi=0.4\\\\H_a:\pi

The significance level is 0.05.

The sample has a size n=50 persons.

The sample proportion is p=0.3.

p=X/n=15/50=0.3

The standard error of the proportion is:

\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.4*0.6}{50}}\\\\\\ \sigma_p=\sqrt{0.0048}=0.069

Then, we can calculate the z-statistic as:

z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.3-0.4+0.5/50}{0.069}=\dfrac{-0.09}{0.069}=-1.299

This test is a left-tailed test, so the P-value for this test is calculated as:

\text{P-value}=P(z

As the P-value (0.097) is greater than the significance level (0.05), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that female employees were passed over for management training in favor of their male colleagues.

b) We have to calculate a 95% confidence interval for the proportion.

The sample proportion is p=0.3.

The standard error of the proportion is:

\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.3*0.7}{50}}\\\\\\ \sigma_p=\sqrt{0.0042}=0.0648

The critical z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

MOE=z\cdot \sigma_p=1.96 \cdot 0.0648=0.127

Then, the lower and upper bounds of the confidence interval are:

LL=p-z \cdot \sigma_p = 0.3-0.127=0.173\\\\UL=p+z \cdot \sigma_p = 0.3+0.127=0.427

The 95% confidence interval for the population proportion is (0.173, 0.427).

The populations proportion (π=0.4) is included in this confidence interval, so the claim has no enough evidence to be supported.

5 0
3 years ago
1/3 + 2/? = 17/24<br><br> fill in the question mark and answer in message box
g100num [7]

Answer:

?=\frac{16}{3}

Step-by-step explanation:

\frac{1}{3}+\frac{2}{?}=\frac{17}{24}

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\frac{?+6}{3?}=\frac{17}{24}

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144=27?

?=\frac{144}{27}

?=\frac{16}{3}

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