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Dmitry [639]
3 years ago
13

The test statistic of zequals2.32 is obtained when testing the claim that pgreater than0.3. a. Identify the hypothesis test as b

eing​ two-tailed, left-tailed, or​ right-tailed. b. Find the​ P-value. c. Using a significance level of alphaequals0.10​, should we reject Upper H 0 or should we fail to reject Upper H 0​?
Mathematics
1 answer:
Sonja [21]3 years ago
6 0

Answer:

a) We need to conduct a hypothesis in order to test the claim that the true proportion p is greatr than 0.3, so then the system of hypothesis are.:  

Null hypothesis:p \leq 0.3  

Alternative hypothesis:p > 0.3  

Right tailed test

b) p_v =P(z>2.32)=0.0102  

c) So the p value obtained was a very low value and using the significance level given \alpha=0.1 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of interest is higher than 0.3

Step-by-step explanation:

Part a: Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion p is greatr than 0.3, so then the system of hypothesis are.:  

Null hypothesis:p \leq 0.3  

Alternative hypothesis:p > 0.3  

Right tailed test

When we conduct a proportion test we need to use the z statisitc, and the is given by:  

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

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

Calculate the statistic  

For this case the statistic is given by z_{calc}= 2.32

Part b: Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be:  

p_v =P(z>2.32)=0.0102  

Part c

So the p value obtained was a very low value and using the significance level given \alpha=0.1 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of interest is higher than 0.3

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Answer:

a=150.7 -0.385*10.2=146.773

So the value of height that separates the bottom 35% of data from the top 65% (Or the 35 percentile) is 146.7.  

Step-by-step explanation:

1) Previous concepts

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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

2) Solution to the problem

Let X the random variable that represent the  scores on the LSAT of a population, and for this case we know the distribution for X is given by:

X \sim N(150.7,10.2)  

Where \mu=150.7 and \sigma=10.2

We want to find a value a, such that we satisfy this condition:

P(X>a)=0.65   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.35 of the area on the left and 0.65 of the area on the right it's z=-0.385. On this case P(Z<-0.385)=0.35 and P(Z>-0.385)=0.65

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

Z=-0.385

And if we solve for a we got

a=150.7 -0.385*10.2=146.773

So the value of height that separates the bottom 35% of data from the top 65% (Or the 35 percentile) is 146.7.  

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Question 13
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The amount to be invested today so as to have $12,500 in 12 years is  $6,480.37.

The amount that would be in my account in 13 years is $44,707.37.

The amount I need to deposit now is $546.64.

<h3>How much should be invested today?</h3>

The amount to be invested today = future value / (1 + r)^nm

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<h3>What is the future value of the account at the end of 13 years?</h3>

Future value = monthly deposits x annuity factor

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<h3>What should be the monthly deposit?</h3>

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Annuity factor = {[(1+r)^n] - 1} / r

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$14,000 / [{(1.0056^24) - 1} / 0.0056] = $546.64

To learn more about annuities, please check: brainly.com/question/24108530

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