Question 1

A company is willing to renew its publishing contract with a popular statistics book author only if he can prove that his book can sell to more than 22% of the entire statistics market.The publishing company contacts 5000 statistics professors at random and only 1050 professors were interested in the book.Should the company renew the contract? Should the company renew the contract? State the critical value required to perform an appropriate hypothesis test using α = 0.01.

Accepted Answer

The answer of A company is willing to renew its...

Question 2

A city claims that 75% of all low income housing is 1500 sq.ft.The tenants believe the proportion of housing this size is smaller than the claim,and hire an independent firm to test a random sample size of 120 and found 1500 sq.ft.housing at 66%.State the critical value required to perform an appropriate hypothesis test using α = 0.001.

Accepted Answer

For a one-tailed test with α = 0.001, the critical value corresponds to the z-score that has 0.001 area in the tail. The negative sign indicates the tenants believe the proportion is smaller, so -3.09 is the correct critical value for α = 0.001 on the left tail of the distribution.

Question 3

Five years ago,a company found that 8% of its employees commuted to work by car.A survey investigates whether the current proportion of employees who commute by car to work is higher than it was five years ago.A test on employee commuting by car was done on a random sample of 1000 employees,and found car commuting to be 12%.Test an appropriate hypothesis using α = 0.05 and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

Accepted Answer

The answer of Five years ago,a company found that 8%...

Question 4

A Science professor has observed over several years that about 15% of the students who initially major in Science drop out of the program after their freshman year.The department head suggested making the curriculum easier by taking a couple of 300 level courses out of the requirements.With the new curriculum in tact,590 began their freshman year as Science majors and only 52 dropped out of the program.Should the college continue with the easier curriculum? State the critical value required to perform an appropriate hypothesis test using α = 0.01.

Accepted Answer

We need to perform a hypothesis test to determine if the proportion of students who dropped out of the program decreased significantly after implementing the easier curriculum. We can use a one-tailed z-test with a level of significance (α) of 0.01.

The null hypothesis is that there is no difference in the proportion of students who drop out of the program before and after the curriculum change:

H0: p1 - p2 = 0

The alternative hypothesis is that the proportion of students who drop out of the program after the curriculum change is significantly lower than before:

Ha: p1 - p2 > 0

where p1 is the proportion of students who dropped out before the curriculum change and p2 is the proportion of students who dropped out after the curriculum change.

We can calculate the test statistic using the formula:

z = (p1 - p2) / sqrt(p*(1-p)*(1/n1 + 1/n2))

where p is the pooled proportion of dropouts, n1 is the sample size before the curriculum change, and n2 is the sample size after the curriculum change.

Before the curriculum change, the proportion of dropouts was 0.15. Out of 590 students who started as Science majors, this means that 0.15*590 = 88.5 dropped out.

After the curriculum change, only 52 students dropped out out of a total of 590. This means the proportion of dropouts was 52/590 = 0.088.

The pooled proportion of dropouts is: 
p = (88.5 + 52) / (590 + 590) = 0.131

The standard error is: 
SE = sqrt(0.131*(1-0.131)*(1/590 + 1/590)) = 0.032

The test statistic is: 
z = (0.15 - 0.088) / 0.032 = 1.9375

The critical value for a one-tailed test with α = 0.01 is -2.326. Since the test statistic (1.9375) is greater than the critical value (-2.326), we fail to reject the null hypothesis.

Therefore, we do not have enough evidence to conclude that the easier curriculum has significantly reduced the proportion of dropouts.

Question 5

A company is willing to renew its publishing contract with a popular calculus book author only if he can prove that his book can sell to more than 15% of the entire calculus market.The publishing company contacts 3000 calculus professors at random and only 420 professors were interested in the book.Should the company renew the contract? State the critical value required to perform an appropriate hypothesis test using α = 0.05.

Accepted Answer

The answer of A company is willing to renew its...

Question 6

According to the 2004 Canadian Community Health Survey,23.1% of Canadians aged 18 or older were considered obese;that is,they had a body mass index (BMI)of 30 more higher.Suppose you believe that the percentage of obese Canadians has increased since 2004 and wish to test your belief.A current survey of 1000 random Canadians found that 245 were obese.Test an appropriate hypothesis using α = 0.10 and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

Accepted Answer

The answer of According to the 2004 Canadian Community Health...

Question 7

A city claims that 75% of all low income housing is 1500 sq.ft.The tenants believe the proportion of housing this size is smaller than the claim,and hire an independent firm to test an appropriate hypothesis.What are the null and alternative hypotheses?

Accepted Answer

The answer of A city claims that 75% of all...

Question 8

A Math professor has observed over several years that about 38% of the students who initially major in Math drop out of the program after their freshman year.The department head suggested making the curriculum easier by taking a couple of 300 level courses out of the requirements.With the new curriculum intact,207 began their freshman year as Math majors and only 59 dropped out of the program.Should the college continue with the easier curriculum? State the critical value required to perform an appropriate hypothesis test using α = 0.05.

Accepted Answer

To determine whether the easier curriculum significantly reduced the percentage of students who drop out of the Math program, we need to perform a hypothesis test. Let p be the proportion of students who drop out of the program with the easier curriculum.

Null Hypothesis: p = 0.38 (the same as before)

Alternative Hypothesis: p < 0.38 (the easier curriculum reduced the dropout rate)

We will use a one-tailed z-test with α = 0.05. The critical z-value for this test is -1.645, as it corresponds to the 5th percentile of the standard normal distribution (since we are testing for a decrease, we use the negative value).

To perform the test, we first calculate the sample proportion of students who dropped out with the easier curriculum:

p̂ = 59/207 ≈ 0.285

Then, we calculate the test statistic:

z = (p̂ - p) / sqrt(p(1-p)/n)
  = (0.285 - 0.38) / sqrt(0.38(1-0.38)/207)
  ≈ -2.24

Since the test statistic falls below the critical value (-1.645), we reject the null hypothesis and conclude that the easier curriculum significantly reduced the percentage of students who dropped out of the Math program.

Question 9

Five years ago,a company found that 8% of its employees commuted to work by car.A survey investigates whether the current proportion of employees who commute by car to work is higher than it was five years ago.A test on employee commuting by car was done on a random sample of 1000 employees,and found car commuting to be 12%.State the critical value required to perform an appropriate hypothesis test using α = 0.001.

Accepted Answer

The answer of Five years ago,a company found that 8%...

Question 10

The management of a water park has concerns about the chlorine level of 0.4% mg/mL increasing to an unsafe level.The management tests the hypothesis that the park's chlorine proportions have remained the same,hat are the null and alternative hypotheses?

Accepted Answer

The answer of The management of a water park has...

Question 11

In April of 2011,the unemployment rate in Canada was reported to be 7.6%.Suppose you wish to conduct a test to determine if the current unemployment rate differs from that of April 2011.What are the null and alternative hypotheses?

Accepted Answer

The answer of In April of 2011,the unemployment rate in...

Question 12

In April of 2011,the unemployment rate in Canada was reported to be 7.6%.You wish to know if the current unemployment rate differs from that of April 2011.You take a random sample size of 1000 and found unemployment at 6.1%.State the critical value required to perform an appropriate hypothesis test using α = 0.05.

Accepted Answer

To perform a hypothesis test regarding the difference in unemployment rates, we use a z-test. With a significance level of 0.05, the critical value for a two-tailed test is 1.96 (found using a standard normal distribution table or calculator). Therefore, if the calculated z-score falls outside of the range -1.96 to 1.96, we can reject the null hypothesis that the current unemployment rate is the same as that of April 2011.

Question 13

According to the 2004 Canadian Community Health Survey,23.1% of Canadians aged 18 or older were considered obese;that is,they had a body mass index (BMI)of 30 more higher.Suppose you believe that the percentage of obese Canadians has decreased since 2004 and wish to test your belief.A current survey of 1000 random Canadians found that 219 were obese.State the critical value required to perform an appropriate hypothesis test using α = 0.05.

Accepted Answer

The hypothesis test is a one-tailed test (testing if the percentage has decreased), and with α = 0.05, the critical value for a left-tailed test is -1.645.

Question 14

A weight loss centre provided a loss for 72% of its participants.The centre's leader decides to test a new weight loss strategy on a random sample size of 140 and found weight loss in 78% of the participants.State the critical value required to perform an appropriate hypothesis test using α = 0.01.

Accepted Answer

The answer of A weight loss centre provided a loss...

Question 15

A city claims that 75% of all low income housing is 1500 sq.ft.The tenants believe the proportion of housing this size is smaller than the claim,and hire an independent firm to test a random sample size of 120 and found 1500 sq.ft.housing at 66%.Test an appropriate hypothesis using α = 0.01 and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

Accepted Answer

The answer of A city claims that 75% of all...

Question 16

In April of 2011,the unemployment rate in Canada was reported to be 7.6%.Suppose that Statistics Canada claims that the current unemployment rate is lower than that of April 2011.Suppose a test was conducted on current unemployment and a random sample size of 1000 and found unemployment at 6.1%.Test an appropriate hypothesis using α = 0.05 and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

Accepted Answer

The answer of In April of 2011,the unemployment rate in...

Question 17

A weight loss centre provided a loss for 72% of its participants.The centre's leader decides to test a new weight loss strategy on a random sample size of 140 and found weight loss in 78% of the participants.Test an appropriate hypothesis using α = 0.05 and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

Accepted Answer

The answer of A weight loss centre provided a loss...

Question 18

A university wants to increase its retention rate of 4% for graduating students from the previous year.After implementing several new programs during the last two years,the university reevaluated its retention rate using a random sample of 352 students and retained 18 students.Should the university continue its new programs? Test an appropriate hypothesis using α = 0.10 and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

Accepted Answer

The answer of A university wants to increase its retention...

Question 19

A university wants to increase its retention rate of 4% for graduating students from the previous year.After implementing several new programs during the last two years,the university reevaluated its retention rate using a random sample of 352 students and retained 18 students.Should the university continue its new programs? State the critical value required to perform an appropriate hypothesis test using α = 0.10.

Accepted Answer

For a one-tailed test with α = 0.10, the critical value from the Z-distribution table is 1.282.

Question 20

A mayor is concerned about the percentage of city residents who express disapproval of his job performance.His political committee pays for a newspaper ad,hoping that it will keep the disapproval rate below 22%.They will use a follow-up poll to assess the ad's effectiveness.

Accepted Answer

The answer of A mayor is concerned about the percentage...

Quiz 20: More About Tests

A city claims that 75% of all low income housing is 1500 sq.ft.The tenants believe the proportion of housing this size is smaller than the claim,and hire an independent firm to test an appropriate hypothesis.What are the null and alternative hypotheses?

The management of a water park has concerns about the chlorine level of 0.4% mg/mL increasing to an unsafe level.The management tests the hypothesis that the park's chlorine proportions have remained the same,hat are the null and alternative hypotheses?

In April of 2011,the unemployment rate in Canada was reported to be 7.6%.Suppose you wish to conduct a test to determine if the current unemployment rate differs from that of April 2011.What are the null and alternative hypotheses?

A mayor is concerned about the percentage of city residents who express disapproval of his job performance.His political committee pays for a newspaper ad,hoping that it will keep the disapproval rate below 22%.They will use a follow-up poll to assess the ad's effectiveness.