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vfiekz [6]
3 years ago
15

In a recent survey, 72 out of 100 consumers reported that they preferred plastic bags instead of paper bags for their groceries.

If there is no difference in the proportions who prefer each type in the population, the chance of such extreme results in a sample of this size is about .03. Because .03 is less than .05, we can conclude that there is a statistically significant difference in preference. Give a numerical value for each of the following.
(a) The p-value.
(b) The level of significance, α.
(c) The sample proportion.
(d) The sample size.
(e) The null value.
Mathematics
1 answer:
kupik [55]3 years ago
3 0

Answer:

a) P=0.03

b) α=0.05

c) 0.72

d) 100

e) 0.72

Step-by-step explanation:

a) The P-value is the probability of the sample result. In this case the P-value is 0.03.

b) The level of significance is the threshold of probabilty for the null hypothesis to be reejcted or not. It is contrasted with the P-value to know if the effect is significant. In this case, the level of significance is 0.05.

NOTE: if it is a two-side test, the level of significance is 0.1 (two times 0.05).

c) The sample proportion is the one that results from the sample data. In this case, the sample proportion is 0.72.

p=72/100=0.72

d) The sample size is the amount of consumers reported. In this case is 100 customers.

e) The null value is 0.72 (equal to the sample proportion), because it is tested if there is no difference between the population proportion and the sample proportion.

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Agata [3.3K]

Answer:

Sin theta = 12/13

Step-by-step explanation:

From the question;

Cot theta = 5/12

Kindly recall;

Cot theta = 1/ tan theta

Hence, tan theta = 12/5

Mathematically

tan theta= opposite/adjacent

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let hypotenuse be h

h^2 = 12^2 + 5^2

h^2 = 144 + 25

h^2 = 169

h = √169

h = 13

But sine theta = opposite/ hypotenuse = 12/13

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3 years ago
How do I turn those numbers into a mixed number?
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3 years ago
Mr.rodriguez invests half money in land a tenth in stocks and a twentieth in bonds he puts the remaining 35,000 in his savings a
Elena-2011 [213]

Answer:  $100,000

<u>Step-by-step explanation:</u>

   Land  +  Stocks  +  Bonds  +  Savings  =  100%

    \dfrac{1}{2}x    +    0.1x     +    \dfrac{1}{20}x       +  35,000   =  1.00x  

=  0.5x   +     0.1x   +     0.05x  +  35,000  =  1.00x

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3 0
3 years ago
Read 2 more answers
The claim that 40% of those persons who retired from an industrial job before the age of 60 would return to work if a suitable j
Bad White [126]

Answer:

The p-value of the test is of 0.1922 > 0.02, which means that there is not significant evidence to reject the null hypothesis, that is, there is not significant evidence to conclude that the proportion is of less than 40%.

Step-by-step explanation:

Test if the proportion is less than 40%:

At the null hypothesis, we test if the proportion is of at least 0.4, that is:

H_0: p \geq 0.4

At the alternative hypothesis, we test if the proportion is of less than 0.4, that is:

H_1: p < 0.4

The test statistic is:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

In which X is the sample mean, \mu is the value tested at the null hypothesis, \sigma is the standard deviation and n is the size of the sample.

0.4 is tested at the null hypothesis:

This means that \mu = 0.4, \sigma = \sqrt{0.4*0.6}

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This means that n = 200, X = \frac{74}{200} = 0.37

Value of the test statistic:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

z = \frac{0.37 - 0.4}{\frac{\sqrt{0.4*0.6}}{\sqrt{200}}}

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P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion below 0.37, which is the p-value of z = -0.87.

Looking at the z-table, z = -0.87 has a p-value of 0.1922.

The p-value of the test is of 0.1922 > 0.02, which means that there is not significant evidence to reject the null hypothesis, that is, there is not significant evidence to conclude that the proportion is of less than 40%.

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Step-by-step explanation:

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