# What Is The Example Of Z Test

*Register to read the introduction…*In addition, this test is used only when the population standard deviation σ is known from a prior source. Finally, data represent a SRS, and measurements that comprise the data are assumed to be accurate and meaningful. Example (“Lake Wobegon”). Garrison Keller claims the children of Lake Wobegon are above average. You take a simple random sample of 9 children from Lake Wobegon and measure their intelligence with a Wechsler test and find the following scores: {116, 128, 125, 119, 89, 99, 105, 116, and 118}. The mean of this sample ( x ) is 112.8. We know Wechsler scores are scaled to be Normally distributed with a mean of 100 and standard deviation of 15. Is this sample mean sufficiently different from a population mean µ of 100 to reject the null hypothesis of “no difference?” The null and alternative hypotheses The claim being made in the illustrative example is that the population has higher than average intelligence. The null hypothesis is the population has average intelligence. Since an average intelligence score is 100, H0: μ = 100. The alternative hypothesis claims the population has a higher than average intelligence. Therefore, H1: μ > 100. (The alternative hypothesis resembles the claim the investigator wishes to bolster.) It would be incorrect

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Alternative hypothesis (H1) - The opposite of the null hypothesis. The hypothesis the researcher hopes to bolster. Alpha (α) - The probability the researcher is willing to take in falsely rejecting a true null hypothesis. Test statistic - A statistic used to test the null hypothesis. P-value - A probability statement that answers the question “If the null hypothesis were true, what is the probability of observing the current data or data that is more extreme than the current data?.” It is the probability of the data conditional on the truth of H0. It is NOT the probability that the null hypothesis is true. Type I error - a rejection of a true null hypothesis; a “false alarm.” Type II error - a retention of an incorrect null hypothesis; “failure to sound the alarm.” Confidence (1 - α) - the complement of alpha. Beta (β) - the probability of a type II error; probability of a retaining a false null hypothesis. Power (1 - β) - the complement of β; the probability of avoiding a type II error; the probability of rejecting a false null