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Thepotemich [5.8K]
3 years ago
9

A significance test is conducted for which the alternative hypothesis states that more than 85 percent of adult sea turtles on a

certain beach are female. The p-value for the test is 0.4158. If the null hypothesis is true, which of the following statements is a correct interpretation of the p-value?
a. Of all possible samples of the same size, 41.58 percent will result in 85 percent of adult sea turtles on the beach being female.
b. Of all possible samples of the same size, 41.58 percent will result in 85 percent or more of adult sea turtles on the beach being female.
c. Of all possible samples of the same size, 41.58 percent will result in 85 percent or less of adult sea turtles on the beach being female.
d. Of all possible samples of the same size, 20.79 percent will result in 85 percent or more of adult sea turtles on the beach being female.
e. Of all possible samples of the same size, 20.79 percent will result in 85 percent of adult sea turtles on the beach being female.
Mathematics
1 answer:
Tcecarenko [31]3 years ago
4 0

Answer:

d. Of all possible samples of the same size, 20.79 percent will result in 85 percent of adult sea turtles on the beach being females.

Step-by-step explanation:

Hypothesis testing is conducted to test an observation against the null hypothesis. P-value is calculated to determine whether to accept or reject the null hypothesis. In the given case the p-value is 0.4158 which means null hypothesis is true.

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You are given the following information obtained from a random sample of 5 observations. 20 18 17 22 18 At 90% confidence, you w
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Answer:

a

  The null hypothesis is  

         H_o  : \mu  =  21

The Alternative  hypothesis is  

           H_a  :  \mu<   21

b

     \sigma_{\= x} =   0.8944

c

   t = -2.236

d

  Yes the  mean population is  significantly less than 21.

Step-by-step explanation:

From the question we are given

           a set of  data  

                               20  18  17  22  18

       The confidence level is 90%

       The  sample  size  is  n =  5  

Generally the mean of the sample  is  mathematically evaluated as

        \= x  =  \frac{20 + 18 +  17 +  22 +  18}{5}

       \= x  =  19

The standard deviation is evaluated as

        \sigma =  \sqrt{ \frac{\sum (x_i - \= x)^2}{n} }

         \sigma =  \sqrt{ \frac{ ( 20- 19 )^2 + ( 18- 19 )^2 +( 17- 19 )^2 +( 22- 19 )^2 +( 18- 19 )^2 }{5} }

         \sigma = 2

Now the confidence level is given as  90 %  hence the level of significance can be evaluated as

         \alpha = 100 - 90

        \alpha = 10%

         \alpha =0.10

Now the null hypothesis is  

         H_o  : \mu  =  21

the Alternative  hypothesis is  

           H_a  :  \mu<   21

The  standard error of mean is mathematically evaluated as

         \sigma_{\= x} =   \frac{\sigma}{ \sqrt{n} }

substituting values

         \sigma_{\= x} =   \frac{2}{ \sqrt{5 } }

        \sigma_{\= x} =   0.8944

The test statistic is  evaluated as  

              t =  \frac{\= x - \mu }{ \frac{\sigma }{\sqrt{n} } }

substituting values

              t =  \frac{ 19  - 21 }{ 0.8944 }

              t = -2.236

The  critical value of the level of significance is  obtained from the critical value table for z values as  

                   z_{0.10} =  1.28

Looking at the obtained value we see that z_{0.10} is greater than the test statistics value so the null hypothesis is rejected

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The fraction \frac{1}{2}>\frac{1}{3} and \frac{1}{2}

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The fraction \frac{1}{2}>\frac{3}{7} and \frac{1}{2}

Thus, \frac{3}{7}

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The length of a rectangle is 3cm longer than its width.If the perimeter of the rectangle is 54cm,find its length in cm.​
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Answer:

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Step-by-step explanation:

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