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Lelechka [254]
2 years ago
7

Suppose that prior to conducting a coin-flipping experiment, we suspect that the coin is fair. How many times would we have to f

lip the coin in order to obtain a 95.8% confidence interval of width of at most .14 for the probability of flipping a head? (note that the z-score was rounded to three decimal places in the calculation)
a) 217
b) 153
c) 212
d) 209
e) 150
f) None of the above
Mathematics
1 answer:
BabaBlast [244]2 years ago
6 0

Answer:

153 times

Step-by-step explanation:

We have to flip the coin in order to obtain a 95.8% confidence interval of width of at most .14

Width = 0.14

ME = \frac{width}{2}

ME = \frac{0.14}{2}

ME = 0.07

ME\geq z \times \sqrt{\frac{\widecap{p}(1-\widecap{p})}{n}}

use p = 0.5

z at 95.8% is 1.727(using calculator)

0.07 \geq 1.727 \times \sqrt{\frac{0.5(1-0.5)}{n}}

\frac{0.07}{1.727}\geq sqrt{\frac{0.5(1-0.5)}{n}}

(\frac{0.07}{1.727})^2 \geq \frac{0.5(1-0.5)}{n}

n \geq \frac{0.5(1-0.5)}{(\frac{0.07}{1.727})^2}

n \geq 152.169

So, Option B is true

Hence  we have to flip 153 times the coin in order to obtain a 95.8% confidence interval of width of at most .14 for the probability of flipping a head

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The desired percentage of SiO2 in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5
miskamm [114]

Answer:  

z=-3.25

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Step-by-step explanation:  

1) Data given and notation  

\bar X=5.24 represent the mean production for the sample  

\sigma=0.32 represent the sample standard deviation for the sample  

n=16 sample size  

\mu_o =5.5 represent the value that we want to test  

\alph=0.05a represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

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

Part a: State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean production is different from 5.5 tons, the system of hypothesis would be:  

Null hypothesis:\mu =5.5  

Alternative hypothesis:\mu \neq 5.5  

If we analyze the info given we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

z=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}} (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic  

We can replace in formula (1) the info given like this:  

z=\frac{5.24-5.5}{\frac{0.32}{\sqrt{16}}}=-3.25  

P-value

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

p_v =2*P(z  

Conclusion  

If we compare the p value and the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the production its significant different compared to the desired percentage of SiO2 of 5.5 at 5% of signficance.  

7 0
2 years ago
For the function h(x) =3x/(x+5)(x-4), solve the equation.​
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Answer:

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Step-by-step explanation:

To 'solve' means to find the x values that make the equation equal zero, so

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Multiply both sides by the denominator to get rid of the fraction

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So x = 0 is the solution for this equation

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Answer:

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Step-by-step explanation:

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If you would like to order the following values in descending order, you can do this using the following steps:

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3 years ago
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Answer:

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<u>If A = 60 then the ratio is</u>

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