The value of the zscores in a hypothesis test is influenced

The value of the z-scores in a hypothesis test is influenced by a variety of factors. Assuming that all other variables are held constant, explain how the value of z is influenced by each of the following: (Hint: When coming up with your answer, consider how changing the corresponding value in the z formula would change things if its value was increased by 10, 100, 1000, etc. while all other values constant.)

Increasing the difference between the sample mean and the original population mean will result in a(n) (increase/decrease) ______ in the absolute value of z, and a(n) (increase/decrease) ______ in the probability of obtaining a sample with that mean.

Increasing the population standard deviation will result in a(n) (increase/decrease) _____in the absolute value of z, and a(n) (increase/decrease) ______in the probability of obtaining a sample with that mean.

Increasing the number of scores in the sample will result in a(n) (increase/decrease) _____ in the absolute value of z, and a(n) (increase/decrease)______in the probability of obtaining a sample with that mean.

Solution

Increasing the difference between the sample mean and the original population mean will result in a(n) (increase/decrease) ______ in the absolute value of z,

[INCREASE], since the numerator\'s absolute value increases.

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and a(n) (increase/decrease) ______ in the probability of obtaining a sample with that mean.

[DECREASE], as this sample become more rare as it goes farther from the population mean.

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Increasing the population standard deviation will result in a(n) (increase/decrease) _____in the absolute value of z,

[DECREASE], as the population standard deviation is at the denominator of z.

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and a(n) (increase/decrease) ______in the probability of obtaining a sample with that mean.

[INCREASE] As z decreases, probability increases.

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Increasing the number of scores in the sample will result in a(n) (increase/decrease) _____ in the absolute value of z,

[INCREASE], as it lessens the standard error.

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and a(n) (increase/decrease)______in the probability of obtaining a sample with that mean.

[DECREASE.] As z increases, probability decreases, signifying a rarer result.