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DENIUS [597]
3 years ago
14

Suppose the null hypothesis, H0, is: a sporting goods store claims that at least 70% of its customers do not shop at any other s

porting goods stores. What is the Type I error in this scenario? a. The sporting goods store thinks that less than 70% of its customers do not shop at any other sporting goods stores when, in fact, less than 70% of its customers do not shop at any other sporting goods stores. b. The sporting goods store thinks that at least 70% of its customers do not shop at any other sporting goods stores when, in fact, at least 70% of its customers do not shop at any other sporting goods stores. c. The sporting goods store thinks that less than 70% of its customers do not shop at any other sporting goods stores when, in fact, at least 70% of its customers do not shop at any other sporting goods stores. d. The sporting goods store thinks that at least 70% of its customers do not shop at any other sporting goods stores when, in fact, less than 70% of its customers do not shop at any other sporting goods stores.
Mathematics
1 answer:
nasty-shy [4]3 years ago
5 0

Answer:

Null hypothesis: p \geq 0.7

Alternative hypothesis: p

A type of error I for this case would be reject the null hypothesis that the population proportion is greater or equal than 0.7 when actually is not true.

So the correct option for this case would be:

c. The sporting goods store thinks that less than 70% of its customers do not shop at any other sporting goods stores when, in fact, at least 70% of its customers do not shop at any other sporting goods stores.

Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".  

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".  

Type I error, also known as a “false positive” is the error of rejecting a null  hypothesis when it is actually true. Can be interpreted as the error of no reject an  alternative hypothesis when the results can be  attributed not to the reality.  

Type II error, also known as a "false negative" is the error of not rejecting a null  hypothesis when the alternative hypothesis is the true. Can be interpreted as the error of failing to accept an alternative hypothesis when we don't have enough statistical power.  

Solution to the problem

On this case we want to test if the sporting goods store claims that at least 70^ of its customers, so the system of hypothesis would be:

Null hypothesis: p \geq 0.7

Alternative hypothesis: p

A type of error I for this case would be reject the null hypothesis that the population proportion is greater or equal than 0.7 when actually is not true.

So the correct option for this case would be:

c. The sporting goods store thinks that less than 70% of its customers do not shop at any other sporting goods stores when, in fact, at least 70% of its customers do not shop at any other sporting goods stores.

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Suppose a random sample of 100 observations from a binomial population gives a value of pˆ = .63 and you wish to test the null h
irakobra [83]

Answer:

We conclude that the population proportion is equal to 0.70.

Step-by-step explanation:

We are given that a random sample of 100 observations from a binomial population gives a value of pˆ = 0.63 and you wish to test the null hypothesis that the population parameter p is equal to 0.70 against the alternative hypothesis that p is less than 0.70.

Let p = <u><em>population proportion.</em></u>

(1) The intuition tells us that the population parameter p may be less than 0.70 as the sample proportion comes out to be less than 0.70 and also the sample is large enough.

(2) So, Null Hypothesis, H_0 : p = 0.70      {means that the population proportion is equal to 0.70}

Alternate Hypothesis, H_A : p < 0.70      {means that the population proportion is less than 0.70}

The test statistics that would be used here <u>One-sample z-test</u> for proportions;

                           T.S. =  \frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }  ~  N(0,1)

where, \hat p = sample proportion = 0.63

            n = sample of observations = 100

So, <u><em>the test statistics</em></u>  =  \frac{0.63-0.70}{\sqrt{\frac{0.70(1-0.70)}{100} } }

                                     =  -1.528

The value of z-test statistics is -1.528.

<u>Now at 0.05 level of significance, the z table gives a critical value of -1.645 for the left-tailed test.</u>

Since our test statistics is more than the critical value of z as -1.528 > -1.645, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u><em>we fail to reject our null hypothesis</em></u>.

Therefore, we conclude that the population proportion is equal to 0.70.

(c) The observed level of significance in part B is 0.05 on the basis of which we find our critical value of z.

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4 0
3 years ago
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1. Over 3 years, how much more does $3000 in a savings account with an APR of 3.2% compounded
Sedbober [7]

Answer:

$1080

Step-by-step explanation:

((3000 \times 0.032) \times 2) \times 3 = 576

convert % to decimal by multiplying 3.2%x100=0.032

then multiply by initial amount 3000x0.032

then multiply by 2 because it's compounding semiannual

then multiply by 3 because it's over a 3 yr period

do the same for the quarterly compound but multiply by 4 because it's quarterly

((3000 \times 0.03) \times 2) \times3 = 1080

over a 3 yr period the quarterly compounded amount will earn:

1080 - 576 = 504

$504 more than the account compounded semiannual

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Latrell and his cousin, Tisha, met at a state park to go for an all-day hike. Latrell drove 122 miles to get to the park, and it
Naddika [18.5K]

Answer:

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Step-by-step explanation:

122/2 is 61

64 plus 32 is 96. 96/1.5 is 64 meaning that she goes 64 miles an hour.

so she goes 3 miles faster on average than latrell, with latrell going 61 an hour average and her going 64 an hour average

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5x^2y

5 is the largest number to go in evenly. And the terms are limited to those. 
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