Mathematics, 14.04.2020 17:52 gatorboy1788

The data given to the right includes data from 37 candies, and 6 of them are red. The company that makes the candy claims that 29% of its candies are red. Use the sample data to construct a 90% confidence interval estimate of the percentage of red candies. What do you conclude about the claim of 29%?

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Answer from: sallonquarts

$0.162 - 1.64\sqrt{\frac{0.162(1-0.162)}{37}}=0.0626$

$0.162 + 1.64\sqrt{\frac{0.162(1-0.162)}{37}}=0.2614$

The 90% confidence interval would be given by (0.0626;0.2614)

For this case since the upper bound of the confidence interval is lower than 29 we have enough evidence to reject the hypothesis that the proportion of red candies is 0.29 or 29%.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Solution to the problem

For this case the estimated proportion of red candies is $\hat p = \frac{6}{37}= 0.162$

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.1$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_{\alpha/2}=-1.64, t_{1-\alpha/2}=1.64$

The confidence interval for the mean is given by the following formula:

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

If we replace the values obtained we got:

$0.162 - 1.64\sqrt{\frac{0.162(1-0.162)}{37}}=0.0626$

$0.162 + 1.64\sqrt{\frac{0.162(1-0.162)}{37}}=0.2614$

The 90% confidence interval would be given by (0.0626;0.2614)

For this case since the upper bound of the confidence interval is lower than 29 we have enough evidence to reject the hypothesis that the proportion of red candies is 0.29 or 29%.

Answer from: Quest

in if you ask questions, the points are taken from your total and given to the one who answered it..

so if i have 30 points and i ask a question for 5 points, then when someone asks a question i will lose 5 points and the answerer earns 5

happy to

Answer from: Quest

Ireally don’t understand your problem do you have a better picture of it

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