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)
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Answer:
The value of the sample mean is 78.
Step-by-step explanation:
We are given that a sample of n = 4 scores is obtained from a population with a mean of 70 and a standard deviation of 8.
Also, the sample mean corresponds to a z score of 2.00.
<em>Let </em><em> = sample mean</em>
The z-score probability distribution for a sample mean is given by;
Z = ~ N(0,1)
where, = population mean = 70
= standard deviation = 8
n = sample size = 4
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
<u>Now, we are given that the sample mean corresponds to a z score of 2.00 for which we have to find the value of sample mean;</u>
So, <em><u>z-score</u></em> formula is given by ;
z-score = =
2.00 =
2.00 =
= 70 + 8 = 78
<em>Therefore, the value of the sample mean is 78.</em>