You wish to test the following claim (Ha) at a significance level of a = 0.002. H.:µ = 71.6 Ha:µ 71.6 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 26 with a mean of a = 82.8 and a standard deviation of s = 16.3. What is the critical value for this test? (Report answer accurate to three decimal places.) critical value = ±2.485 What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = 3.503 The test statistic is... in the critical region not in the critical region
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
I only need help with the marked sections, I'm not sure what went wrong? Thank you!
From the provided information,
Sample size (n) = 26
Sample mean (x̅) = 82.8
Sample standard deviation (s) = 16.3
Level of significance (α) = 0.002
Hypotheses are as follow:
H0: µ = 71.6
Ha: µ ≠ 71.6
The test is two tailed.
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