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Cloud [144]
4 years ago
5

The area of the trapezoid is 75 cm2. What is the height of the trapezoid? ______ cm

Mathematics
1 answer:
ivanzaharov [21]4 years ago
6 0
The height of the trapezoid is 37cm

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Find the value of x.
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2 years ago
The concentration of active ingredient in a liquid laundry detergent is thought to be affected by the type of catalyst used in t
Paha777 [63]

Answer:

The 95% confidence interval would be given by -5.980 \leq \mu_1 -\mu_2 \leq -0.720  

p_v =2*P(Z

Step-by-step explanation:

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_1 =65.2 represent the sample mean 1

\bar X_2 =68.55 represent the sample mean 2

n1=10 represent the sample 1 size  

n2=10 represent the sample 2 size  

s_1 =3.55 sample standard deviation for sample 1

s_2 =2.29 sample standard deviation for sample 2

\sigma =3 represent the population standard deviation

\mu_1 -\mu_2 parameter of interest.

Part a

The confidence interval for the difference of means is given by the following formula:  

(\bar X_1 -\bar X_2) \pm z_{\alpha/2}\sqrt{\sigma^2(\frac{1}{n_1}+\frac{1}{n_2})} (1)  

The point of estimate for \mu_1 -\mu_2 is just given by:

\bar X_1 -\bar X_2 =65.2-68.55=-3.35

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 tabel to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that z_{\alpha/2}=1.96  

The standard error is given by the following formula:

SE=\sqrt{\sigma^2(\frac{1}{n_1}+\frac{1}{n_2})}

And replacing we have:

SE=\sqrt{3^2(\frac{1}{10}+\frac{1}{10})}=1.342

Confidence interval

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

-3.35-1.96\sqrt{3^2(\frac{1}{10}+\frac{1}{10})}=-5.980  

-3.35+1.96\sqrt{3^2(\frac{1}{10}+\frac{1}{10})}=-0.720  

So on this case the 95% confidence interval would be given by -5.980 \leq \mu_1 -\mu_2 \leq -0.720  

If the system of hypothesis are given by:

Null Hypothesis:\mu_1 -\mu_2=0

Alternative hypothesis:\mu_1 -\mu_2 \neq 0

The statistic would be:

z=\frac{\bar X_1 -\bar X_2 -0}{\sqrt{\sigma^2(\frac{1}{n_1}+\frac{1}{n_2})}}

And if we replace we got:

z=\frac{65.2 -68.55 }{\sqrt{3^2(\frac{1}{10}+\frac{1}{10})}}=-2.497

And the p value would be given by:

p_v =2*P(Z

And with 5% of significance we have enough evidence to reject the null hypothesis since the p_v < \alpha

5 0
3 years ago
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