Answer:
The critical value of t 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:
H₀: μ = μ₀ vs. H₀: μ ≠ μ₀
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 t-test for single mean.
The test statistic is defined as follows:
[tex]t_{cal.}=\frac{\bar x-\mu}{s/\sqrt{n}}\sim t_{\alpha/2, (n-1)}[/tex]
The information given is:
n = 55
α = 0.01
Compute the critical value of t as follows:
[tex]t_{\alpha/2, (n-1)}= t_{0.01/2, (55-1)}=t_{0.005, 54}=2.66[/tex]
*Use a t-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 t at 0.01 level of significance is 2.66.
