What critical value of t* should be used for a 95% confidence interval for the population mean based upon a random sample of 20 observations?

t* = 1.725
t* = 1.729
t* = 2.086
t* = 2.093

Respuesta :

To find the degrees of freedom in the given question, we have to take into consideration of the confidence interval as well as degrees of freedom. The critical t-value in this data set is 2.086

What is Confidence Interval?

This is the range of values that we observe in our sample and for which we expect to find the value that accurately reflects the population.

We can also say that it is a range of values so defined that there is a specified probability that the value of a parameter lies within it.

Data;

  • sample size (n) = 20
  • degree of freedom (df) = n-1 = 20 - 1 = 19

At 95% confidence level, the t is

[tex]\alpha = 1 - 95% = 1 - 0.95 = 0.05\\\frac{\alpha }{2} = \frac{0.05}{2} = 0.025\\t_\frac{\alpha }{2}_,_d_t = t_0_._0_2_5_,_2_0 = 2.086[/tex]

The critical t-value in this data set is 2.086

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