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Bogdan [553]
2 years ago
8

A rectangular prsim has a volume of 144 cubic yards. The height of the prism is 12 yards, and the width of the prism is 2 yards.

Caculate the length of the prism.
Mathematics
1 answer:
STALIN [3.7K]2 years ago
8 0
Volume=length*width*height
Volume is 144
Height is 12
Width is 2
144=L*2*12
144=L*24
144/24=L
6=L
Length is 6 yards
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p_v =2*P(t_{40}>0.505)=0.61633  

Comparing the p value with the significance level \alpha=0.05 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, then the difference between the two groups is NOT significantly different.  

Step-by-step explanation:

Data given and notation

\bar X_{1}=162 represent the mean for sample of clinic attendees

\bar X_{2}=156 represent the mean for the sister city  

s_{1}=41 represent the sample standard deviation for 1  

s_{2}=36 represent the sample standard deviation for 2  

n_{1}=22 sample size for the group 2  

n_{2}=20 sample size for the group 2  

\alpha=0.05 Significance level provided

t would represent the statistic (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to check if the difference in the population means, the system of hypothesis would be:  

Null hypothesis:\mu_{1}-\mu_{2}=0  

Alternative hypothesis:\mu_{1} - \mu_{2}\neq 0  

We don't have the population standard deviation's, so for this case is better apply a t test to compare means, and the statistic is given by:  

t=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}} (1)  

And the degrees of freedom are given by df=n_1 +n_2 -2=22+20-2=40  

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.  

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

t=\frac{(162-156)-0}{\sqrt{\frac{41^2}{22}+\frac{36^2}{20}}}}=0.505  

P value  

Since is a bilateral test the p value would be:  

p_v =2*P(t_{40}>0.505)=0.61633  

Comparing the p value with the significance level \alpha=0.05 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, then the difference between the two groups is NOT significantly different.  

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