Help please math problem

According to the University of Nevada Center for Logistics Management, of all merchandise sold in the United States gets returne

Step2247 [10]

Answer:

a) $\hat p=\frac{12}{80}=0.15$ estimated proportion of items that were returned

b) The 95% confidence interval would be given (0.0718;0.228).

c) Using a significance level assumed $\alpha=0.05$ we see that $p_v$ so we have enough evidence at this significance level to reject the null hypothesis. And on this case makes sense the claim that the proportion of returns at the Houston store significantly different from the returnsfor the nation as a whole.

Step-by-step explanation:

Assuming:

According to the University of Nevada Center for Logistics Management, 6% of all mer-chandise sold in the United States gets returned. Houston department store sampled 80 items sold in January and found that 12 of the items were returned.

Data given and notation

n=80 represent the random sample taken

X=12 represent the items that were returned

$\hat p=\frac{12}{80}=0.15$ estimated proportion of items that were returned

$\alpha=0.05$ represent the significance level (no given, but is assumed)

Confidence =0.95 or 95%

p= population proportion of items that were returned

a. Construct a point estimate of the proportion of items returned for the population ofsales transactions at the Houston store

$\hat p=\frac{12}{80}=0.15$ estimated proportion of items that were returned

b. Construct a 95% confidence interval for the porportion of returns at the Houston store

The confidence interval would be given by this formula

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

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$0.15 - 1.96 \sqrt{\frac{0.15(1-0.15)}{80}}=0.0718$

$0.15 + 1.96 \sqrt{\frac{0.15(1-0.15)}{80}}=0.228$

And the 95% confidence interval would be given (0.0718;0.228).

c. Is the proportion of returns at the Houston store significantly different from the returns for the nation as a whole? Provide statistical support for your answer.

We need to conduct a hypothesis in order to test the claim that the population proportion differs significantly to the USA proportion of 6% or no. We have the following system of hypothesis :

Null Hypothesis: $p = 0.06$

Alternative Hypothesis: $p \neq 0.06$

We assume that the proportion follows a normal distribution.

This is a two tailed test for the proportion .

The One-Sample Proportion Test is "used to assess whether a population proportion $\hat p$ is significantly (different,higher or less) from a hypothesized value $p_o$ ".

Check for the assumptions that he sample must satisfy in order to apply the test

a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.

b) The sample needs to be large enough

$np_o =80*0.15=12>10$

$n(1-p_o)=80*(1-0.15)=68>10$

Calculate the statistic

The statistic is calculated with the following formula:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o(1-p_o)}{n}}}$

On this case the value of $p_o=0.06$ is the value that we are testing and n = 80.

$z=\frac{0.15 -0.06}{\sqrt{\frac{0.06(1-0.06)}{80}}}=3.390$

The p value for the test would be:

$p_v =2*P(z>3.390)=0.00070$

Using a significance level assumed $\alpha=0.05$ we see that $p_v$ so we have enough evidence at this significance level to reject the null hypothesis. And on this case makes sense the claim that the proportion of returns at the Houston store significantly different from the returnsfor the nation as a whole.

5 0

4 years ago

If f (x) - 3(x + 5) +-, what is f(a + 2)?

sergey [27]

Answer:

A

Step-by-step explanation:

Just plug in $x=a+2$ .

4 0

3 years ago

To a box that contained 30 pencils 10 out of which were red several more non-red pencils were added. Now 25% of all pencils in t

Anastasy [175]

Answer:

The Amount of Non-red pencil which were added to the box = 10

Step-by-step explanation:

Given as :

The number of pencils in a box = 30

The number of red pencils in a box out of 30 = 10

So , the number of Non-red pencils = 30 - 10 = 20

Again let the number of Non-red pencils which added further = x

So, now the amount of total pencil get increase to (30+x)

Among (30+x) pencils in box,25% of them are red ,

I.e The number of red pencils in a box out of (30+x) = 25% of (30+x)

And the number of Non-red pencils = 20 + x

SO, according to question

25% of (30+x) + (20+x) = (30+x)

Or, (20+x) = (30+x) - (25% of (30+x))

Or, 20+x = (30+x) [ 1 -( $\frac{25}{100}$ ]

Or, 20+x = (30+x) ( $\frac{3}{4}$

Or, 80+4x = 90+3x

or 4x - 3x = 90-80

Or, x = 10

Hence the number of Non-Red pencils in the box which added further = 10 Answer

4 0

3 years ago

What does 64/100 represent as a ratio and a percent

Dvinal [7]

64/100 is easy its just 64 out of 100

7 0

3 years ago

What is the gcf of 18 and 42!!?

nadya68 [22]

The gcf of 18 and 42 is the largest positive integer that divides the numbers 18 and 42 without a remainder. Spelled out, it is the greatest common factor of 18 and 42. Here you can find the gcf of 18 and 42, along with a total of three methods for computing it.

7 0

3 years ago

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