Question

In: Math

In a poll of 1000 randomly selected prospective voters in a local election, 281 voters were...

In a poll of 1000 randomly selected prospective voters in a local election, 281 voters were in favor of a school bond measure.

a. What is the sample proportion? Type as: #.###

b. What is the margin of error for the 90% confidence level? Type as: #.###

c. What is the margin of error for the 95% confidence level? Type as: #.###

d. What is the 95% confidence interval? Type as: [#.###, #.###]

A poll reported a 36% approval rating for a politician with a margin of error of 1 percentage point.

a. How many voters must be sampled for a 90% confidence interval? Round up to the nearest whole number.

b. How many voters must be sampled for a 95% confidence interval? Round up to the nearest whole number.

Intelligence quotient (IQ) test scores are believed to have a mean of 100 and a population standard deviation of 15. In a random sample of 36 students in a high school, the mean IQ test score is 105. Researchers claim that the mean IQ test scores at this high school is statistically higher than 100.

a. What is the hypothesized mean?

b. Is the hypothesis test two-tailed, right-tailed, or left-tailed? Type as: two-tailed, left-tailed, or right-tailed

c. What is the z-score?

d. What is the p-value? Type as: #.#####

A transportation commission studies driving times between two cities to determine whether the construction of a new highway reduced commute times. Times for 40 cars driving on the old highway and times for 50 cars driving on the new highway are obtained. A summary of the data obtained from the study is given below.

Highway Mean commute times Population standard deviation
1 (Old) 5.35 0.5
2 (New) 4.95 0.8

a. What is the standard error? Type as: #.###

b. What is the z-score? Type as: #.###

c.What is the p-value? Type as: #.######

10,000 individuals are divided evenly into two groups. The treatment group is given a vaccine and the control group is given a placebo. 95 of the 5,000 individuals in the treatment group developed a disease. 125 of the 5,000 individuals in the control group developed a particular disease. A research team wants to determine whether the vaccine is effective in decreasing the incidence of disease. Does sufficient evidence exist to conclude that the proportion of developing a disease in individuals given the vaccine is less than that of individuals given a placebo?

a. What is the proportion of individuals in the treatment group that developed the disease? Type as: #.###

b. What is the proportion of individuals in the control group that developed the disease? Type as: #.###

c. What is the proportion of individuals in the overall group that developed the disease? Type as: #.###

d. What is the standard error estimate? Type as: #.####

e. What is the z-score? Type as: #.###

f. What is the p-value? Type as: #.####

Solutions

Expert Solution

1)

In a poll of 1000 randomly selected prospective voters in a local election, 281 voters were in favor of a school bond measure.

a. The sample proportion is,

b. The margin of error for the 90% confidence level is,

For 90% confidence level z critical value = 1.645

c. The margin of error for the 95% confidence level is,

For 95% confidence level z critical value = 1.96

d. The 95% confidence interval is,

2)

A poll reported a 36% approval rating for a politician with a margin of error of 1 percentage point.

a. The sample size is obtained using the formula,

For 90% confidence level z critical value = 1.645

p = 0.36

margin of error = 1% of p = 0.036

b. The sample size is obtained using the formula,

For 90% confidence level z critical value = 1.96

p = 0.36

margin of error = 1% of p = 0.036

3)

a. Hypothesized mean = 100

b. right-tailed

c. The z-score is obtained using the formula (population standard deviation is known),

d. The p-value is obtained from z distribution table for z = 2

4)

a. The standard error is obtained using the formula (population standard deviation is known),

b. The z-score is,

c. The p-value is obtained from z distribution table for z = 2.8981

milcah answered 1 year ago
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