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Dafna1 [17]
3 years ago
9

i need with this math problem. I am confused on how to do it. If you could help me it would be great. There are 2 parts to this

problem. I need help with both problems. 

Mathematics
1 answer:
Novay_Z [31]3 years ago
4 0
She took a total of 60 minutes
she answered both mulitiple choice and extended response in the total time which is 60 minutes
she took 2 minutes on rach multiple choice question and 6 minutes for the extended response
let x=number of multiple choice questions
let y=number of extended response questions
we can deduce that
total time =x*2+y*6
60=2x+6y
also we can deduce
20=x+y
since 20 ia the sum of multiple choice and extended response
for part 2 we just solve the system of equations
60=2x+6y
20=x +y
lets multiply the second equation by 2 so we can get rid of x
60=2x+6y
40=2x+2y
subtracting the two equations from each other to yields
20=0 +4y
y=5
to get x we substitute in one of the equations we derived from question 1
x+y=20
substituting y for its value we get
x+5=20
x=15
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Regarding the hypothesis tested in this problem, it is found that:

a) The test statistic is: t = 0.49.

b) The p-value is: 0.6297..

c) The null hypothesis is not rejected, as the p-value is greater than the significance level.

d) It appears that the students are legitimately good at estimating one minute, as the sample does not give enough evidence to reject the null hypothesis.

<h3>What is the test statistic?</h3>

The test statistic of the t-distribution is given by the equation presented as follows:

t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}

In which the variables of the equation are given as follows:

  • \overline{x} is the sample mean.
  • \mu is the value tested at the hypotheses.
  • s is the standard deviation of the sample.
  • n is the sample size.

The value tested at the hypothesis is:

\mu = 60

From the sample, using a calculator, the other parameters are given as follows:

\overline{x} = 62.47, s = 19.2, n = 15

Hence the test statistic is obtained as follows:

t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}

t = \frac{62.47 - 60}{\frac{19.2}{\sqrt{15}}}

t = 0.49.

<h3>What are the p-value and the conclusion?</h3>

The p-value is obtained using a t-distribution calculator, with a two-tailed test, as we are testing if the mean is different a value, in this case 60, with:

  • 15 - 1 = 14 df, as the number of degrees of freedom is one less than the sample size.
  • t = 0.49, as obtained above.

Hence the p-value is of 0.6297.

Since the p-value is greater than the significance level of 0.01, the null hypothesis is not rejected, attesting to the ability of the students to estimate one minute.

More can be learned about the test of an hypothesis at brainly.com/question/13873630

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