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shepuryov [24]
3 years ago
9

What is the measure of

Mathematics
1 answer:
Liula [17]3 years ago
5 0

The angle of NPR is 130°

First, set up an equation to find x.

(3x-10)+2x+65=180

Then, solve the equation for x.

x=25

Then, substitute 25 in for x in 2x

50

Finally, subtract 50 from 180 to find the angle of NPR

130°

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To find a missing angle on your calculator, hit the 2nd button, then the tan button and enter in 7.7/14 and hit enter.  You should get an angle measure of 28.8°

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z=\frac{5.2-5.1}{\frac{0.6}{\sqrt{210}}}=2.415  

The critical region would be (1.28; \infty)  

p_v =P(Z>2.415)=0.00786  

If we compare the p value and a significance level given \alpha=0.1 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 true mean is higher than 5.1 pounds/square inch at 10% of significance.  

Step-by-step explanation:

Data given and notation  

\bar X=5.2 represent the average score for the sample  

\sigma=0.6 represent the population standard deviation  

n=210 sample size  

\mu_o =5.1 represent the value that we want to test  

\alpha=0.1 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)  

State the null and alternative hypotheses.  

We need to apply a one upper tailed test.  

What are H0 and Ha for this study?  

Null hypothesis: \mu \leq 5.1  

Alternative hypothesis :\mu > 5.1  

Compute the test statistic  

The statistic for this case is given by:  

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\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{5.2-5.1}{\frac{0.6}{\sqrt{210}}}=2.415  

Critical value

On this case since we have a right tailed test we need to look into the normal standard distribution and find a value that accumulates 0.1 of the area on the right of the distribution or 0.9 of the area on the left and for this case we see that z_{critical}=1.28

The critical region would be (1.28; \infty)  

Give the appropriate conclusion for the test  

Since is a one side upper tailed test the p value would be:  

p_v =P(Z>2.415)=0.00786  

Conclusion  

If we compare the p value and a significance level given \alpha=0.1 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 true mean is higher than 5.1 pounds/square inch at 10% of significance.  

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3 years ago
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