Which method will not work?

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

2 years ago

A rubber ball has a radius of about 2.86 in. Can the ball be packaged in a box shaped like a cube with a volume of 125 in3?

Vlada [557]

Answer:

I am not sure what the values needed to add in / etc, but here is the height of the box: 5

Step-by-step explanation:

A cube is a kind of rectangle where all the sides are the same. So to find volume, cube the length of any side. To find height, calculate the cube root of a cube's volume. For this example, the cube has a volume of 125. The cube root of 125 is 5. The height of the cube is 5.

(hopefully this is correct, have a nice day!)

6 0

2 years ago

Round to the nearest thousand then subtract

dsp73

100

6738 —> 7000
5903 —> 6000

7000 - 6000 = 1000

6 0

3 years ago

If 90 percent of automobiles in Orange County have both headlights working, what is the probability that in a sample of eight au

Alex17521 [72]

Answer:

$P(X \geq 7) = P(X=7) +P(X=8)$

And we can find the individual probabilities using the probability mass function

$P(X=7)=(8C7)(0.9)^7 (1-0.9)^{8-7}=0.3826$

$P(X=8)=(8C8)(0.9)^8 (1-0.9)^{8-8}=0.4305$

And replacing we got:

$P(X \geq 7) = P(X=7) +P(X=8)=0.3826 +0.4305=0.8131$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest "number of automobiles with both headligths working", on this case we now that:

$X \sim Binom(n=8, p=0.9)$