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Tanzania [10]
2 years ago
15

Suppose you are going to conduct a two tail test concerning the population mean. Suppose that you do not know what the populatio

n standard deviation is and that you have a sample of 55 observations. If you are going to conduct this test at the .01 level of significance what is the critical value?

Mathematics
1 answer:
IRINA_888 [86]2 years ago
4 0

Answer:

The critical value of <em>t</em> at 0.01 level of significance is 2.66.

Step-by-step explanation:

The hypothesis for the two-tailed population mean can be defined as:

<em>H₀</em>: <em>μ </em>= <em>μ₀</em> vs. <em>H₀</em>: <em>μ </em>≠ <em>μ₀</em>

It is provided that the population standard deviation is not known.

Since there is no information about the population standard deviation, we will use a <em>t</em>-test for single mean.

The test statistic is defined as follows:

t_{cal.}=\frac{\bar x-\mu}{s/\sqrt{n}}\sim t_{\alpha/2, (n-1)}

The information given is:

<em>n</em> = 55

<em>α</em> =<em> </em>0.01

Compute the critical value of <em>t</em> as follows:

t_{\alpha/2, (n-1)}= t_{0.01/2, (55-1)}=t_{0.005, 54}=2.66

*Use a <em>t</em>-table for the value.

If the desired degrees of freedom are not provided consider he next highest degree of freedom.

Thus, the critical value of <em>t</em> at 0.01 level of significance is 2.66.

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