Description
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A z-test is any statistical test otherwise known as a hypothesis for which the distribution of the test statistic under the null hypothesis can be approximated by a normal distribution ("Z-test," 2018). A one-sample location test, two-sample location test, paired difference test and maximum likelihood estimate are examples of tests that can be conducted as z-tests. Z-tests are closely related to t-tests, but a z-test assumes the standard deviation is known and the sample size is large.
The reason a z-test would be preferred over a t-test is when an investor wishes to test whether the average daily return of a stock is greater than 1%. A simple random sample of 50 returns is calculated and has an average of 2%. Assume the standard deviation of the returns is 2.50%. Therefore, the null hypothesis is when the average, or mean, is equal to 3%. The alternative hypothesis is whether the mean return is greater than 3%. Assume an alpha of 0.05% is selected with a two-tailed test. Consequently, there is 0.025% of the samples in each tail, and the alpha has a critical value of 1.96 or -1.96. If the value of z is greater than 1.96 or less than -1.96, the null hypothesis is rejected. Nuisance parameters should be known or estimated with high accuracy. Z-tests focus on a single parameter, and treat all other unknown parameters as being fixed at their true values ("Z-test," 2018). Z-tests are not commonly used because it is not as straightforward or easy to use compared to t-tests.
References
Z-test. (2018). In Wikipedia. Retrieved October 8, 2018, from https://en.wikipedia.org/wiki/Z-test
Explanation & Answer
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Running head: PART 6 TOPIC 3 DQ1
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Part 6 Topic 3 DQ1
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PART 6 TOPIC 3 DQ1
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Part 6 Topic 3 DQ1
The two statistical tests used to compare mean values and decide on whether or not there
is a significant difference between them are the z-test and the t-test. In this regard, these tests are
useful to compare either the mean of two different samples between them or the mean of the
sample with the expected mean of the population. These tests use the bell-shaped standard and tdistributions as a way to evaluate the probability of overlapping of the two mean values
compared. While researchers often use the z-test as an approximation to the t-test, it is necessary
to understand the differences and similarities to know when such approximation may be justified.
In this regard, as stated in the discussion post, one of the most essential requisites for the
decision among which test to use is the population standard deviation. Thus, if the researcher
knows the value of the standard deviation of the population or can use a reasonable estimate for
it, it is possible to use the z-test. Howeve...
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