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Ira Lisetskai [31]
3 years ago
7

A store owner is interested in opening a second shop. She wants to estimate the true average daily revenue of her current shop t

o decide whether expanding her business is a good idea. The store owner takes a random sample of 60 days over a six-month period and finds that the mean revenue of those days is 3,472.00 dollars with variance 315,900.20 square dollars. Calculate a 95% confidence interval to estimate the true average daily revenue.
Mathematics
1 answer:
Alex3 years ago
6 0
Every confidence interval has associated z value. As confidence interval increases so do the z value associated with it. 
The confidence interval can be calculated using following formula:
\overline{x} \pm \frac{zs}{\sqrt n}
Where \overline{x} is the mean value, z is the associated z value, s is the standard deviation and n is the number of samples.
We know that standard deviation is simply a square root of variance:
s=\sqrt{315900.20}=\$562.05
The confidence interval of 95% has associated z value of <span>1.960.
</span>Now we can calculate the confidence interval for our income:
3472.00\pm \frac{1.960\cdot 562.05}{\sqrt{60}}\\ \$3472.00\pm142.22


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Answer:

<em>Test statistic </em>

<em>               </em>t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }  

            t = <em>1.076</em>

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given Mean of the Population (μ) = 8.0

<em>Mean of the sample (x⁻) = 8.25</em>

Given data

                  8,9,9,8,8,9,8,7

Given sample size  n= 8

Given sample standard deviation(S) = 0.661

<u><em>Step(ii):-</em></u>

<em>Null hypothesis : H:  (μ) = 8.0</em>

<em>Alternative Hypothesis :H:(μ) > 8.0</em>

<em>Degrees of freedom = n-1 = 8-1=7</em>

<em>Test statistic </em>

<em>               </em>t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }<em></em>

<em>              </em>t = \frac{8.25 -8.0}{\frac{0.661}{\sqrt{8} } }<em></em>

<em>            t =  1.076</em>

<em>Critical value </em>

<em>                    t₍₇,₀.₀₅₎   = 2.3646</em>

<em>The calculated value   t =  1.076 < 2.3646 at 0.05 level of significance</em>

<em>Null hypothesis is accepted</em>

<em>Test the hypothesis that the true mean quiz score is 8.0 against the alternative that it is not greater than 8.0</em>

<em></em>

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Answer:

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Step-by-step explanation:

We are given that

50+\frac{1}{2}m=120

We have to find who is correct and explain.

We know that

Equation: It is mathematical sentence that combines  numbers and variables which shows the equality of two expressions.

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Example:

x+y

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It is in equation form.

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