Question 1

$X\sim B(10,0.65)$. Find $P(X>3)$, correct to 4 decimal places.

Accepted Answer

$$0.9740$$

Answer

$$0.9051$$

Answer

$$0.0212$$

Answer

$$0.0260$$

Question 2

Marian is an archer. When she shoots an arrow at a target, there is a probability of 0.4 that she hits the bull. What is the probability, to 3 significant figures, that she hits the bull exactly 6 times when she shoots 16 arrows?

Accepted Answer

$$0.198$$

Answer

$$0.527$$

Answer

$$0.802$$

Answer

$$0.473$$

Question 3

Marian is an archer. When she shoots an arrow at a target, there is a probability of 0.4 that she hits the bull. What is the probability, to 3 significant figures, that she hits the bull at least 5 times  times when she shoots 10 arrows?

Accepted Answer

$$0.367$$

Answer

$$0.833$$

Answer

$$0.167$$

Answer

$$0.633$$

Question 4

Marian is an archer. When she shoots an arrow at a target, there is a probability of 0.4 that she hits the bull. She is invited to a charity event where she shoots 20 arrows at a target. Every time she hits the bull she will raise £50 for charity. Calculate the expected donation.

Accepted Answer

£400

Answer

£8

Answer

£1000

Answer

£20

Question 5

The probability that patients have to wait more than 15 minutes in a health practice is 0.3. One of the doctors claim there is a decrease in the number of patients that have to wait more than 15 minutes.  What is the alternative hypothesis?

Accepted Answer

$$H_1: p<0.3$$

Answer

$$H_1: p
eq0.3$$

Answer

$$H_1: p>0.3$$

Answer

$$H_1: p=0.3$$

Question 6

The probability that patients have to wait more than 15 minutes in a health practice is 0.3. One of the doctors claim there is a decrease in the number of patients that have to wait more than 15 minutes.  He records the waiting times of 20 patients. What is the critical region at the 5% level?

Accepted Answer

$$X\leq2$$

Answer

$$X\geq10$$

Answer

$$X\leq2 \cup X\geq10$$

Answer

$$X\leq1 \cup X\geq10$$

Question 7

The probability that patients have to wait more than 15 minutes in a health practice is 0.3. One of the doctors claim there is a decrease in the number of patients that have to wait more than 15 minutes.  For the critical region, what is the actual significance level?

Accepted Answer

$$0.0354$$

Answer

$$0.05$$

Answer

$$0.025$$

Answer

$$0.354$$

Question 8

The probability that patients have to wait more than 15 minutes in a health practice is 0.3. One of the doctors claim there is a decrease in the number of patients that have to wait more than 15 minutes.  He records the waiting times for the next 20 patients and 3 wait more than 15 minutes. Is there evidence to support the doctor? Write your conclusion.

Accepted Answer

Accept $$H_0$$. There is not enough evidence to support the doctor.

Answer

Accept $$H_0$$. There is enough evidence to support the doctor.

Answer

Reject $$H_0$$. There is not enough evidence to support the doctor.

Answer

Reject $$H_0$$. There is enough evidence to support the doctor.

Question 9

The probability that James wins at chess against his computer is 0.4. He says he has improved his game. In the next 8 games he wins 6. What is the test statistic?

Accepted Answer

$$X$$ - The number of games James wins.

Answer

The Binomial Distribution.

Answer

$$H_0:p=0.4$$

Answer

$$X=6$$ James wins $$6$$ games.

Question 10

The probability that James wins at chess against his computer is 0.4. He says he has improved his game. In the next 8 games he wins 6. Find, at the 5% significance level, the critical region to test if James' game has improved?

Accepted Answer

$$X\geq6$$

Answer

$$X\leq5$$

Answer

$$X=0$$

Answer

$$X\geq5$$

Question 11

The probability that James wins at chess against his computer is 0.4. He says he has improved his game. In the next 8 games he wins 6. Using the critical region $$X\geq6$$ what is your conclusion?

Accepted Answer

Reject $$H_0$$. There is enough evidence to suggest James' game has improved.

Answer

He needs to practice more!

Answer

Reject $$H_1$$. There is enough evidence to suggest James' game has improved.

Answer

$$6$$ is in the critical region so reject $$H_0$$.

Question 12

A company has mixed sweets delivered with 70% red and the rest blue. The company wishes to test whether there has been a change in the ratio of blue to red sweets. To do this, they take a sample of 20 sweets of which 9 are red. Does this indicate a change at 5% significance?

Accepted Answer

Yes. Critical Region is $$X\leq9 \cup X\geq19$$. As $$9$$ lies in the critical region so reject $$H_0$$ suggesting a change in the ratio of sweets.

Answer

Yes, Critical Region is $$X\leq9 \cup X\geq18$$.  As $$9$$ lies in the critical region so reject $$H_0$$ suggesting a change in the ratio of sweets.

Answer

No. Critical Region is $$X<9 \cup X\geq18$$. As $$9$$ lies outside the critical region so accept $$H_0$$ suggesting no change in the ratio of sweets.

Answer

Yes, Critical Region is $$X\leq10 \cup X\geq18$$. As $$9$$ lies in the critical region so reject $$H_0$$ suggesting a change in the ratio of sweets.

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