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3 years ago

How do I get EF in question 12

Mathematics

1 answer:

Zinaida [17]3 years ago

8 0

Check the picture below.

since the arcEF is 75°, then the central angle it is in is also 75°, and the radius is of course 2.4,

$\bf \textit{arc's length}\\\\
s=\cfrac{\theta \pi r}{180}~~
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad degrees\\
------\\
r=2.4\\
\theta =75
\end{cases}\implies s=\cfrac{(75)(\pi )(2.4)}{180}\implies s=\pi$

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The mean cost of a meal for two in a mid-range restaurant in Tokyo is $40 (Numbeo.com website, December 14, 2014). How do prices

NNADVOKAT [17]

Answer:

a) $Me=2.02 \frac{6.827}{\sqrt{42}}=2.13$

b) So on this case the 95% confidence interval would be given by (30.53;34.79)

c) On this case the confidence interval not contains the price $40, so we can conclude that the prices for Hong Kong mid-range restaurants are significant less than the prices for mid range restaurants in Tokyo at 5 % of significance.

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

2) Part a

The margin of error is given by:

$Me=t_{\alpha/2}\frac{s}{\sqrt{n}}$

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=42-1=41$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,41)".And we see that $t_{\alpha/2}=2.02$

$Me=2.02 \frac{6.827}{\sqrt{42}}=2.13$

3) Part b

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=32.66$

The sample deviation calculated $s=6.827$

Now we have everything in order to replace into formula (1):

$32.66-2.02\frac{6.827}{\sqrt{42}}=30.532$

$32.66+2.02\frac{6.827}{\sqrt{42}}=34.788$

So on this case the 95% confidence interval would be given by (30.532;34.788)

4) Part d

On this case the confidence interval not contains the price $40, so we can conclude that the prices for Hong Kong mid-range restaurants are significant less than the prices in mid range restaurants in Tokyo at 5 % of significance.

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3 years ago

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Answer:

1. 186 hundredths/2

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