Homework answers / question archive / Question 1 If you roll a pair of fair dice, what is the probability of each of the following? (round all answers to 4 decimal ) a) getting a sum of 1? B) getting a sum of 5?  c) getting a sum of 12?   Question 2 You are conducting a study to test a claim that the mean income of regular casino visitors is significantly less than $50,000

Question 1 If you roll a pair of fair dice, what is the probability of each of the following? (round all answers to 4 decimal ) a) getting a sum of 1? B) getting a sum of 5?  c) getting a sum of 12?   Question 2 You are conducting a study to test a claim that the mean income of regular casino visitors is significantly less than $50,000

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Question 1

If you roll a pair of fair dice, what is the probability of each of the following? (round all answers to 4 decimal )

a) getting a sum of 1?

B) getting a sum of 5? 

c) getting a sum of 12?

 

Question 2

You are conducting a study to test a claim that the mean income of regular casino visitors is significantly less than $50,000. A random sample of 55 regular casino visitors had a mean income of $47,865. Do the sample data provide convincing evidence to support the claim? Assume 0 is known to be $24,000. Conduct a hypothesis test using a 1% level of significance. Give numeric answers to at least 2 decimal places.

What are the correct hypotheses? (Select the correct symbols and values.)

H₀:  Select an answer

H₁ : Select an answer

Based on the hypotheses, find the following:

 Test Statistic =

Critical-value =   

 

The correct decision is to  =Select an answer

The correct conclusion would be:  Select an answer 

significantly less than S50,000 that the mean income of regular casino visitors is

 

Question 3

The annual rainfall in a certain region is approximately normally distributed with mean 42.5 inches and standard deviation 5.5 inches. Round answers to the nearest tenth of a percent.

a) What percentage of years will have an annual rainfall of less than 44 inches?

b) What percentage of years will have an annual rainfall of more than 40 inches?

c) What percentage of years will have an annual rainfall of between 38 inches and 43 inches?

 

 

 

Question 4

H₀ : µ ≥ 42.3

H₁ : µ < 42.3

Your sample consists of 39 values, with a sample mean of 41.4. Suppose the population standard deviation is known to be 3.37.

a) Calculate the value of the test statistic, rounded.) 2 decimal places. z =

b) At a= 0.03, the rejection region is

O z > 2.17

O z <-1.08

O z < -1.88 or z > 1.88

O z < -2.17

O z < -2.17 or z > 2.17

O z > 1.88

C) The decision is to

0 Fait to reject the null hypothesis

O Accept the null hypothesis

O Reject the null hypothesis

O Accept the alternative hypotheis

d) Supposed you mistakenly failed to reject the null hypothesis in this problem, what type of error is that,

0 Type I

0 Type II

 

Question 5

According to a study, 90 % of adult smokers started smoking before 21 years old. 5 smokers 21 years old or older are randomly selected, and the number of smokers who started smoking before 21 is recorded.

1. The probability that at least 3 of them started smoking before 21 years of age is

2. The probability that at most 3 of them started smoking before 21 years of age is

3. The probability that exactly 3 of them started smoking before 21 years of age is

Question 6

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately o^- = 21.3. You would like to be 95% confident that your estimate is within 0.1 of the true population mean. How large of a sample size is required?  

n=

  

Do not round mid-calculation. However, use a critical z value accurate to two (2) decimal places.

 

Question 7

The number of people who survived the Titanic based on class and gender is in the following table. Suppose a person is picked at random from the survivors.

Class	Female	Male	Total
1st	134	59	193
2nd	93	26	119
3rd	80	57	137
Total	307	142	449

 

a) What is the probability that a survivor was female? Round final answer to 3 decimal places.

 

b) What is the probability that a survivor was in the 1st class? Round final answer to 3 decimal places.

 

c) What is the probability that a survivor was a female given that the person was in 1^st class Round final answer to 3 decimal places.

 

d) What is the probability that a survivor was, female and in the 1^st class

Round final answer to 3 decimal places.

 

e) What is the probability that a survivor was a female of in the 1st class?

Round final answer to 3 decimal places.

 

f) Are the events "survivor is a female” and "survivor is in 1st class independent?

Why or why not?

 

 

Question 8

If n = 20, x^- = 45, and g = 12, construct a confidence interval at a 80 % confidence level. Assume the data came from a normally distributed population.

Give your answers to one decimal place.

                <µ<                                       

 

Question 9

In conducting the hypothesis test below, your sample consists of 26 observations, with a mean of 45.4 and standard deviation of 4.8.

H₀ : µ ≥ 46.2

H₁ : µ ≥ 46.2

a) This is a 

b) Calculate the test statistic, rounded to 3 decimal places. t= 

c) At a = 0.05, the rejection region is

0 t < -2.06 or t > 2.06

0 t > 1.708

0 t <-1.708

O none of the above

d) The decision is to

0 fail to reject H₁ since the test statistic does not fall in the rejection region.

0 reject H₁ since the test statistic falls in the rejection region.

0 fail to reject H₀ since the test statistic does not fall in the rejection region.

0 reject H₀ since the test statistic falls in the rejection region.

0 none of the above

 

• Question 10

A population of values has a normal distribution with µ = 334.7 and a = 9.5. You intend to draw a random sample of size n = 19. Round z to two (2) decimal places and final answer to 4 decimal places.

Find the probability  that a single randomly selected value is less than 340.4.

 P(x < 340.4) =

Find the probability( that a sample of size n = 19 is randomly selected with a mean less than 340.4.

P(x^- < 340.4) =

 

Question 11 Suppose (16, 44 ) is a 99% confidence interval estimate for a population mean µ)

A) The point estimate X^- is

b) The margin of error is I

c) Which of the following are tr. statements?

I. There is a 0.99 probability that µ is between 16 and 44.

ii. There's a 99% chance that any particular value in the population will fall between 16 and 44.

III. 99% of confidence intervals constructed in this population will have a lower limit of 16 and an upper limit of 44.

IV. if 99% confidence intervals are calculated from all possible samples of the given size, µ  is expected to be in 99% of these intervals.

0 I and III

0 I and 11

0 IV only

0 I and IV

0 III only

0 II and III

 

Question 14

A hypothesis test was conducted to investigate whether the population mean age of college students at Osler city is higher than 22.

a) This is a

0 left-tailed test. 0 two-tailed test.

0 right-tailed test. 0 half -way test.

b) Select a correct formulation of the appropriate hypotheses:

0 H₀: µ =22                           O H₀ : µ ≥ 22                        O H₀ : µ < 22

   H₁ : µ ≠ 22)                       H₁ : µ < 22                            H₁ : µ ≥ 22

 

O H₀ : µ > 22        O H₀ : µ ≤ 22                        O H₀ : µ ≠ 22

   H₁ : µ ≤ 22             H₁ : µ > 22                        H₁ : µ = 22

 

Question 13

Match each of the following statements with the terms and values below:

0 A single statistic that is used to estimate a population parameter

0 Failure to reject a false null hypothesis

0 (Upper confidence limit - Lower confidence limit)/2

0 1-a

0 If we reject H₀ at a = 0.03 we must also reject it at

0 If we fail to reject H₀ at a = 0.04 we must also fail to reject it at

0 Rejecting H₀: µ ≤ 24 when in fact µ =22

0 The sampling distribution of the sample mean becomes approximately normal as n becomes large

0 The decision when the test statistic falls outside the critical region

0 A range of values of to sample statistic that likely contains the population parameter

 

a. a = 0.02

b. Type II error

c. Central Limit Theorem

d. Type I error

e. a = 0.06

f. Confidence interval

g. Margin of error

h. Confidence level

I. Point estimate

J. Fail to reject H₀