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Schach [20]
3 years ago
10

On a 40 question test students gain 6 points for each correct answer and lose 0.5 points on each incorrect answer. If everyone r

equired to give an answer to each question, what is the formulas that describes how a student's raw score, r, depends on the number of correct answers he or she provided, c?
Mathematics
1 answer:
juin [17]3 years ago
7 0

Answer:

\text{r}=5.5\text{c}-20

Step-by-step explanation:

GIVEN: On a 40 question test students gain 6 points for each correct answer and lose 0.5 points on each incorrect answer. If everyone required to give an answer to each question.

TO FIND: the formulas that describes how a student's raw score, r, depends on the number of correct answers he or she provided, c.

SOLUTION:

Total number of incorrect questions =40-\text{c}

Total marks deducted due to incorrect question =(40-\text{c})\times0.5=20-0.5\text{c}

Total correct questions =\text{c}

Total marks scored =6\text{c}

Total raw marks \text{r}=\text{total marks gained}-\text{total marks deducted}

                           \text{r}=6\text{c}-(20-0.5\text{c})

                           \text{r}=5.5\text{c}-20

ormulas that describes how a student's raw score, r, depends on the number of correct answers he or she provided, c is  \text{r}=5.5\text{c}-20

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Answer:

a) Null Hypothesis: \mu =900

Alternative hypothesis: \mu \neq 900

b) The 95% confidence interval would be given by (910.05;959.95)    

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Step-by-step explanation:

a. State the hypotheses.

On this case we want to check the following system of hypothesis:

Null Hypothesis: \mu =900

Alternative hypothesis: \mu \neq 900

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\mu population mean (variable of interest)

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The confidence interval for the mean is given by the following formula:

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}   (1)

In order to calculate the mean and the sample deviation we can use the following formulas:  

\bar X= \sum_{i=1}^n \frac{x_i}{n} (2)  

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Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that z_{\alpha/2}=1.96

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935+1.96\frac{180}{\sqrt{200}}=959.95    

So on this case the 95% confidence interval would be given by (910.05;959.95)    

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Since we confidence interval not ocntains the value of 900 we fail to reject the null hypothesis that the true mean is 900.

d. What is the p-value?

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If we replace we got:

z=\frac{935 -900}{\frac{180}{\sqrt{200}}}=2.750

Since is a bilateral test the p value is given by:

p_v =2*P(Z>2.750)=0.0059

So then since the p value is less than the significance we can reject the null hypothesis at 5% of significance.

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