Mathematics, 19.03.2020 19:45 harmony000011

A genetic experiment with peas resulted in one sample of offspring that consisted of 423 green peas and 159 yellow peas. a. Construct a 90% confidence interval to estimate of the percentage of yellow peas. b. It was expected that 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not 25%, do the results contradict expectations?

Answers: 1

Show answers

Answers

Answer from: moran14

a) $0.273 - 1.64\sqrt{\frac{0.273(1-0.273)}{582}}=0.243$

$0.273 + 1.64\sqrt{\frac{0.273(1-0.273)}{582}}=0.303$

The 90% confidence interval would be given by (0.243;0.303)

b) For this case since the confidence interval contains the value of 0.25 we don't have enough evidence to conclude that the true proportion of yellow peas is not 25%, so then the null hypothesis that the value expected of 25% for yellow peas can't be rejected at 10% of significance.

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".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

Part a

We can estimate the proportion of yellow peas like this:

$\hat p = \frac{159}{423+159} = 0.273$

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:

$0.273 - 1.64\sqrt{\frac{0.273(1-0.273)}{582}}=0.243$

$0.273 + 1.64\sqrt{\frac{0.273(1-0.273)}{582}}=0.303$

The 90% confidence interval would be given by (0.243;0.303)

Part b

For this case since the confidence interval contains the value of 0.25 we don't have enough evidence to conclude that the true proportion of yellow peas is not 25%, so then the null hypothesis that the value expected of 25% for yellow peas can't be rejected at 10% of significance.

Answer from: Quest

what do you need me to answer?

step-by-step explanation:

Answer from: Quest

option a is correct.

$\frac{\text{original height}}{\text{original base}}=\frac{\text{reduction height}}{\text{reduction base}}$

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have

$\frac{\text{original height}}{\text{original base}}=\frac{\text{reduction height}}{\text{reduction base}}$

Which is the scale factor proportion for the reduction shown? answers are on picture.

Another question on Mathematics

Mathematics, 21.06.2019 17:30

It takes jonas 7 1/4 minutes to run the mile. it takes mario 8 5/12 to run the mile. how much faster is jonas than mario? 5/6 minute 1 1/3 minutes 1 1/6 minutes 1 1/2 minutesi will give points and brainlest

Answers: 2

Answer

Mathematics, 21.06.2019 19:00

Which statement best explains why ben uses the width hi to create the arc at j from point k

Answers: 2

Answer

Mathematics, 21.06.2019 19:00

When keisha installed a fence along the 200 foot perimeter of her rectangular back yard, she left an opening for a gate.in the diagram below, she used x to represent the length in feet of the gate? what is the value? a. 10 b. 20 c. 25 d. 30

Answers: 1

Answer

Mathematics, 21.06.2019 19:30

Prove the divisibility of the following numbers: 25^9 + 5^7 is divisible by 30.also, read as (25 to the power of 9) + (5 to the power of 7) is divisible by 30. blank x 30what is the blank? ( it should be expressed in exponent form)

Answers: 1

Answer

You know the right answer?

A genetic experiment with peas resulted in one sample of offspring that consisted of 423 green peas...

Questions