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Bond [772]
2 years ago
11

Find the value for the side marked below.

Mathematics
1 answer:
olga55 [171]2 years ago
6 0

Answer:

Solution given:

angle : 80°

hypotenuse:y=?

opposite=21

we have

Sin 80=\frac{opposite} {hypotenuse}=\frac{21}{y}

doing crisscrossed multiplication

we get

y=\frac{21}{Sin 80°}

<u>y=21.32</u>

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Answer:

We conclude that the mean amount packaged is equal to 8.17 ounces.

Step-by-step explanation:

We are given that in a particular sample of 50 packages, the mean amount dispensed is 8.171 ​ounces, with a sample standard deviation of 0.052 ounces.

Let \mu = <u><em>population mean amount packaged. </em></u>

So, Null Hypothesis, H_0 : \mu = 8.17 ounces    {means that the mean amount packaged is equal to 8.17 ounces}

Alternate Hypothesis, H_A : \mu\neq 8.17 ounces    {means that the mean amount packaged is different from 8.17 ounces}

The test statistics that will be used here is <u>One-sample t-test statistics</u> because we don't know about the population standard deviation;

                               T.S.  =  \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }  ~  t_n_-_1

where, \bar X = sample mean amount dispensed = 8.171 ounces

             s = sample standard deviation = 0.052 ounces

            n = sample of packages = 50

So, <u><em>the test statistics</em></u> =  \frac{8.171-8.17}{\frac{0.052}{\sqrt{50} } }  ~   t_4_9

                                    =  0.1359  

The value of t-test statistics is 0.1359.

<u>Also, the P-value of test-statistics is given by;</u>

the meaning of the​ p-value is that the p-value is the probability of obtaining a sample mean that is equal to or more extreme than 0.001 ounces away from8.17 if the null hypothesis is true.

                    P-value = P( t_4_9 > 0.136) = More than 40% {from the t-table}

Since the P-value of our test statistics is more than the level of significance of 0.01, so <u><em>we have insufficient evidence to reject our null hypothesis</em></u> as it will not fall in the rejection region.

Therefore, we conclude that the mean amount packaged is equal to 8.17 ounces.

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Hello there!

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