Could someone PLEASE help me on this?

Assume that you plan to use a significance level of alpha α equals =0.05 to test the claim that p 1 p1 equals = p 2 p2. Use the

stiks02 [169]

Answer:

z=3.536

$\hat p=0.204$

$p_v =2*P(Z>3.54)\approx 0.0004$

Step-by-step explanation:

1) Data given and notation

$X_{1}=172$ represent the number of people with the characteristic 1

$X_{2}=356$ represent the number of people with the characteristic 2

$n_{1}=677$ sample 1 selected

$n_{2}=3377$ sample 2 selected

$p_{1}=\frac{172}{677}=0.254$ represent the proportion estimated for the sample 1

$p_{2}=\frac{654}{3377}=0.194$ represent the proportion estimated for the sample 2

$\hat p$ represent the pooled estimate of p

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

$\alpha=0.05$ significance level given

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if is there is a difference between the two proportions, the system of hypothesis would be:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{172+654}{677+3377}=0.204$

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

3) Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.254-0.194}{\sqrt{0.204(1-0.204)(\frac{1}{677}+\frac{1}{3377})}}=3.536$

4) Statistical decision

Since is a two side test the p value would be:

$p_v =2*P(Z>3.54)\approx 0.0004$

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to to reject the null hypothesis, and we can say that the proportion analyzed is significantly different between the two groups.

6 0

4 years ago

An appliance store is having a 25% off sale on Black Friday. Which of the following could be deals offerend by the store during

cluponka [151]

Answer:

refrigerator and dryer

4 0

3 years ago

The exam had 60 questions.Phelix got 85% correct. How many questions did he answer correctly?

hichkok12 [17]

Y is 85% of 60

Equation: Y = P% * X

Solving our equation for Y
Y = P% * X
Y = 85% * 60

Converting percent to decimal:
p = 85%/100 = 0.85

Y = 0.85 * 60
Y = 51

6 0

3 years ago

Read 2 more answers

A publisher reports that 65% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is

muminat

Answer:

$z=\frac{0.60 -0.65}{\sqrt{\frac{0.65(1-0.65)}{340}}}=-1.933$

The p value for this case can be calculated with this probability:

$p_v =2*P(z$

For this case is we use a significance level of 5% we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion is different from 0.65 or 65%. We need to be careful since if we use a value higher than 65 for the significance the result would change

Step-by-step explanation:

Information given

n=340 represent the random sample taken

$\hat p=0.60$ estimated proportion of readers owned a laptop

$p_o=0.65$ is the value that we want to test

z would represent the statistic

$p_v{/tex} represent the p valueHypothesis to testWe want to check if the true proportion of readers owned a laptop if different from 0.65
Null hypothesis:[tex]p=0.65$

Alternative hypothesis: $p \neq 0.65$

The statistic is given by:

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

Replacing we got:

$z=\frac{0.60 -0.65}{\sqrt{\frac{0.65(1-0.65)}{340}}}=-1.933$

The p value for this case can be calculated with this probability:

$p_v =2*P(z$

For this case is we use a significance level of 5% we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion is different from 0.65 or 65%. We need to be careful since if we use a value higher than 65 for the significance the result would change

5 0

4 years ago

What is 19.19 rounded to the nearest tenth

Aleks04 [339]

19.2 because the 0.09 changes the 0.1 to a 0.2

8 0

3 years ago

Read 2 more answers