Consider the following hypothesis test. H0: ? = 30 Ha: ? ≠ 30 The population standard deviation is 15. Use ? = 0.05. How large a sample should be taken if the researcher is willing to accept a 0.10 probability of making a type II error when the actual population mean is 34? The sample size for a two-tailed hypothesis test for a population mean be
Consider the following hypothesis test.
H0: ? = 30
Ha: ? ≠ 30
The population standard deviation is 15. Use ? = 0.05.
How large a sample should be taken if the researcher is willing to accept a 0.10 probability of making a type II error when the actual population mean is 34?
The
z?/2
is the z-value that corresponds to an upper tail area of
| ? |
| 2 |
,
z?
is the z-value that corresponds to an upper tail area of ?, ? is the population standard deviation,
?0
is the hypothesized population mean, and
?a
is the population mean used for the type II error.
n =
| (z?/2 + z?)2?2 |
| (?0 − ?a)2 |
We are told to use ? = 0.05, so
| ? |
| 2 |
= . The researcher is willing to accept a probability of 0.10 of making a type II error, so
? = .
Use technology to find the values of
z?/2
and
z?,
rounding each to two decimal places.
z?/2
=
z?
=
The population standard deviation was given to be 15, so we have
? = .
If the actual population mean is 34, the researcher is willing to accept a type II error of 0.10 for the following hypotheses.
| H0: ? = 30 |
| Ha: ? ≠ 30 |
Thus,
?0 =
and
?a = .
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