Question

Researcher found that fifth-grade students completed more mathematics problems correctly when simple problems were mixed in with their regular math assignments. In order to test this hypothesis, a researcher selects a standardized mathematics achievement test that produces a normal distribution of scores with a mean of μ = 100 and standard deviation of σ =18. The researcher modifies the test by inserting a set of very easy problems among the standardized questions, and gives the modified test to a sample of n = 36 students. If the average test score for the sample is M = 104, (Use α = .01), figure the 99% of confidence interval (Do not need to conduct a hypothesis test)

Answer 1

96.275 < µ < 111.725

Explanation:

For our sample:

n = 36, x = 104

The population standard deviation is: σ = 18

We need a 99% confidence interval. Since our sample size is greater than 30, we use the z-score of 2.575.

See attached photo for construction of confidence interval