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3 0

3 years ago

1. The data given below includes data from 42 candies, and 7 of them are red. The company that makes the candy claims that 33%

jeyben [28]

Answer:

The 95% confidence interval for true proportion of red candies is (5%, 27%).

The true proportion of red candies made by the company is different from 33%.

Step-by-step explanation:

The hypothesis to determine whether the claim made by the candy company is correct or not is:

H₀: The true proportion of red candies made by the company is 33%, i.e. p = 0.33.

Hₐ: The true proportion of red candies made by the company is different from 33%, i.e. p ≠ 0.33.

A (1 - α)% confidence interval can be constructed to check this claim.

The decision rule is:

If the confidence interval consists the null value then the null hypothesis will not be rejected. Otherwise it will be rejected.

The (1 - α)% confidence interval for population proportion is:

$CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

The information provided is:

n = 42

X = number of red candies = 7

Compute the sample proportion of candies that are red as follows:

$\hat p=\frac{X}{n}=\frac{7}{42}=0.167$

The critical value of z for 95% confidence level is:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use a z-table for the critical value.

Compute the 95% confidence interval for true proportion of red candies as follows:

$CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.167\pm 1.96\times \sqrt{\frac{0.167(1-0.167)}{42}}\\=0.16\pm0.1137\\=(0.0463, 0.2737)\\\approx(0.05, 0.27)$

The 95% confidence interval for true proportion of red candies is (5%, 27%).

The confidence interval does not contains the null value.

Thus, the null hypothesis will be rejected at 5% level of significance.

Conclusion:

The true proportion of red candies made by the company is different from 33%.

7 0

3 years ago

There are 416 students who are enrolled in an introductory geology course. if there are seven boys to every six girls, how many

Alenkinab [10]

$\text{Let the number of boys be x and number of girls be y.}\\
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\text{and there are total 416 students enrolled in the course. so we have}\\
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x+y=416 \ \ \ \ \ \ \ \ \ \ ......(i)\\
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\text{also given that there are seven boys to every six girls, that is}\\
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\frac{x}{y}=\frac{7}{6}$

$\Rightarrow 6x=7y\\
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\Rightarrow y=\frac{6x}{7}\\
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\text{substitute this value of y in (i), we get}\\
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x+\frac{6x}{7}=416\\
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\Rightarrow \frac{7x+6x}{7}=416\\
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\Rightarrow \frac{13x}{7}=416\\
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\Rightarrow x=\frac{416\times 7}{13}\\
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\Rightarrow x=224$