The z-test Flashcards
What is the term used to describe a hypothesis test?
z-test
When do we use the z-test?
Whenever we want to check if a sample mean we have is different from some population mean
Visiting aliens form Ziltoidia 10 pride themselves on their performance in our puny human IQ test. As a population their IQ scores follow a normal distribution: N(125, 10). In particular the Ziltoidian president (Zdave) is very proud and hypothesises that the 16 members of his elite Ziltoidian Special Advisory Group (Z-SAG) would perform particularly well on average even compared to the Zitoidian population.
The Z-SAG visits your IQ lab one day and ask you to undertake an experiment to test President Zdave’s hypothesis using a z-test (they really like the name of this test by the way). The sample mean IQ for Z-SAG (including the president) is 127.
Choose the most appropriate null and research hypotheses for this experiment.
a.
H0: The Z-SAG sample came from a population with mean equation image indicator > 125
H1: The Z-SAG sample came from a population with mean equation image indicator = 125
b.
H0: The Z-SAG sample came from a population with mean equation image indicator = 125
H1: The Z-SAG sample came from a population with mean equation image indicator ≠ 125
c.
H0: The Z-SAG sample came from a population with mean equation image indicator < 125
H1: The Z-SAG sample came from a population with mean equation image indicator > 125
d.
H0: The Z-SAG sample came from a population with mean equation image indicator = 125
H1: The Z-SAG sample came from a population with mean equation image indicator > 125
D
Visiting aliens form Ziltoidia 10 pride themselves on their performance in our puny human IQ test. As a population their IQ scores follow a normal distribution: N(125, 10). In particular the Ziltoidian president (Zdave) is very proud and hypothesises that the 16 members of his elite Ziltoidian Special Advisory Group (Z-SAG) would perform particularly well on average even compared to the Zitoidian population.
The Z-SAG visits your IQ lab one day and ask you to undertake an experiment to test President Zdave’s hypothesis using a z-test (they really like the name of this test by the way). The sample mean IQ for Z-SAG is 127.
What is the standard deviation of the SDM (i.e. the standard error) for samples of the same size as Z-SAG
a. 0.625 b. 10 c. 2.5 d. 12.5
SDM SD or s.e. = pop. SD / SQRT (sample size)
SDM SD or s.e. = 10 / SQRT (16)
SDM SD or s.e. = 2.5
Answer = C
Visiting aliens form Ziltoidia 10 pride themselves on their performance in our puny human IQ test. As a population their IQ scores follow a normal distribution: N(125, 10). In particular the Ziltoidian president (Zdave) is very proud and hypothesises that the 16 members of his elite Ziltoidian Special Advisory Group (Z-SAG) would perform particularly well on average even compared to the Zitoidian population.
The Z-SAG visits your IQ lab one day and ask you to undertake an experiment to test President Zdave’s hypothesis using a z-test (they really like the name of this test by the way). The sample mean IQ for Z-SAG (including the president) is 127.
What is the z-statistic that will enable you to test the research hypothesis?
a. 0.8 b. 0.2 c. 3.2 d. 0.16
SDM SD or s.e. = pop. SD / SQRT (sample size)
SDM SD or s.e. = 10 / SQRT (16)
SDM SD or s.e. = 2.5
z score = (x - mean) / SDM SD or s.e.
z score = (127 - 125) / 2.5
z score = 0.80
Answer = A
Visiting aliens form Ziltoidia 10 pride themselves on their performance in our puny human IQ test. As a population their IQ scores follow a normal distribution: N(125, 10). In particular the Ziltoidian president (Zdave) is very proud and hypothesises that the 16 members of his elite Ziltoidian Special Advisory Group (Z-SAG) would perform particularly well on average even compared to the Zitoidian population.
The Z-SAG visits your IQ lab one day and ask you to undertake an experiment to test President Zdave’s hypothesis using a z-test (they really like the name of this test by the way). The sample mean IQ for Z-SAG (including the president) is 127.
Part 4 (of 4):
What is the p-value associated with the z-statistic you calculated in the last question? Based on this p-value what should you do?
a. p = 0.4207 We should not reject the null because p > 0.05 b. p = 0.0007 We should reject the null because p < 0.05 c. p = 0.2119 We should not reject the null because p > 0.05 d. p = 0.4364 We should not reject the null because p > 0.05
SDM SD or s.e. = pop. SD / SQRT (sample size)
SDM SD or s.e. = 10 / SQRT (16)
SDM SD or s.e. = 2.5
z score = (x - mean) / SDM SD or s.e.
z score = (127 - 125) / 2.5
z score = 0.80
p value = 0.2119
p > 0.05
Fail to reject H0
Answer = C
