Question

In: Statistics and Probability

Suppose we are interested in the mean scores on an exam. A random sample of 36...

Suppose we are interested in the mean scores on an exam. A random sample of 36 scores is taken and gives a sample mean (sample mean score) of 68 (x̄ = 68). In this example, we have the unusual knowledge that the population standard deviation is 3 points. Do not count on knowing the population parameters outside of textbook examples.

Find a 90% confidence interval for the true (population) mean of statistics exam scores.

Expert Solution

Solution :

Given that,

Z_/2 = 1.645

Margin of error = E = Z_/2* ( / $\sqrt$ n)

= 1.645 * (3 / $\sqrt$ 36)

= 0.82

At 90% confidence interval estimate of the population mean is,

- E < < + E

68 - 0.82 < < 68 + 0.82

67.18 < < 68.82

(67.18 , 68.82)

orchestra answered 2 years ago

We take a random sample of 16 scores from a Math Exam and the sample mean...

We take a random sample of 16 scores from a Math Exam and the sample mean is 80 (the population scores are normally distributed) . The known standard deviation = 16. What is the value of Lower Confidence Limit at 90% CI.

A) Suppose that the mean and standard deviation of the scores on a statistics exam are...

A) Suppose that the mean and standard deviation of the scores on a statistics exam are 89.2 and 6.49, respectively, and are approximately normally distributed. Calculate the proportion of scores below 77. 1) 0.0301 2) 0.9699 3) We do not have enough information to calculate the value. 4) 0.2146 5) 0.7854 B) When students use the bus from their dorms, they have an average commute time of 8.974 minutes with standard deviation 3.1959 minutes. Approximately 66.9% of students reported a...

Suppose the scores of students on an exam are normally distributed with a mean of 340...

Suppose the scores of students on an exam are normally distributed with a mean of 340 and a standard deviation of 57. Then according to the Empirical Rule approximately 99.7 of the exam scores lie between the integers and .

1. The average of a random sample of 10 scores on a college placement exam is...

1. The average of a random sample of 10 scores on a college placement exam is x ¯= 75, and the sample standard deviation is s = 8.4. Assuming that the collection of all scores on the exam is approximately normally distributed, find a 90 percent confidence interval for the mean score. 2. In a random sample of 100 eligible voters, 85 preferred candidate A over candidate B. Find a 99 percent confidence interval for the proportion p of voters...

A sample of final exam scores is normally distributed with a mean equal to 29 and...

A sample of final exam scores is normally distributed with a mean equal to 29 and a variance equal to 25. Part (a) What percentage of scores are between 24 and 34? (Round your answer to two decimal places.) Part (b) What raw score is the cutoff for the top 10% of scores? (Round your answer to one decimal place.) Part (c) What is the proportion below 23? (Round your answer to four decimal places.) Part (d) What is the...

A sample of final exam scores is normally distributed with a mean equal to 25 and...

A sample of final exam scores is normally distributed with a mean equal to 25 and a variance equal to 16. Part (a) What percentage of scares are between 21 and 29? (Round your answer to two decimal places) Part (b) What raw score is the cutiff for the top 10% of scores? (Round your answer to one decimal place) Part (c) What is the proportion below 20? (Round your answer to four decimal places) Part (d) What is the...

A sample of final exam scores is normally distributed with a mean equal to 24 and...

A sample of final exam scores is normally distributed with a mean equal to 24 and a variance equal to 25. Part (a) What percentage of scores are between 19 and 29? (Round your answer to two decimal places.) % Part (b) What raw score is the cutoff for the top 10% of scores? (Round your answer to one decimal place.) Part (c) What is the proportion below 18? (Round your answer to four decimal places.) Part (d) What is...

A sample of final exam scores is normally distributed with a mean equal to 26 and...

A sample of final exam scores is normally distributed with a mean equal to 26 and a variance equal to 16. (a) What percentage of scores are between 22 and 30? (Round your answer to two decimal places.) (b)What raw score is the cutoff for the top 10% of scores? (Round your answer to one decimal place.) (c)What is the proportion below 19? (Round your answer to four decimal places.) (d)What is the probability of a score less than 33?...

A sample of final exam scores is normally distributed with a mean equal to 23 and...

A sample of final exam scores is normally distributed with a mean equal to 23 and a variance equal to 16. Part (a) What percentage of scores are between 19 and 27? (Round your answer to two decimal places.) Part (b) What raw score is the cutoff for the top 10% of scores? (Round your answer to one decimal place.) Part (c) What is the proportion below 17? (Round your answer to four decimal places.) Part (d) What is the...

Suppose we are interested to construct a confidence interval of the mean test score. A random...

Suppose we are interested to construct a confidence interval of the mean test score. A random sample of 36 scores is taken and gives a sample mean (sample mean score) of 68. We know that the population standard deviation is 3 points. EBM will be the largest at? a. for a 66% confidence level b. for a 95% confidence level c. for a 99% confidence level d. for a 90% confidence level