A hypothesis will be used to test that a population mean equals 7 against the alternative that the population mean does not equal 7 with known variance σ. What are the critical values for the test statistic Upper Z Subscript 0 for the significance level of 0.04? Round your answer to two decimal places (e.g. 98.76).

For a two-sided test like this (the mean can be significantlt greater or smaller than 7 to reject the null hypothesis), the critical values are the values of z that determine the boundaries of rejecting or not the null hypothesis.

If the significance level is 0.04, it means that there is a P-value of 0.02 for z larger than the upper critical value z₀.

[tex]P(z>z_0)=\alpha /2= 0.02[/tex]

If we look up in a normal distribution table, the z value that corresponds to this probability is z=2.05.

topeadeniran2 topeadeniran2 · Answer 2 · 2022-03-25T15:31:59+01:00

The upper critical value z₀ of the hypothesis is 2.05.

How to explain the hypothesis?

From the information given, it can be noted that this is a two-sided test. In this case, the critical values are the values of z that determine the boundaries of whether one should reject the null hypothesis or shouldn't.

Since the significance level is 0.04, it simply implies that there is a p-value of 0.02. Then, the next thing is to check the normal distribution table, and this corresponds to the z value of 2.05.

In conclusion, the correct option is 2.05.

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