Question

# x = 24.4, s = 9.2, n = 25, Ho: µ = 26, Ha: µ <...

x = 24.4, s = 9.2, n = 25, Ho: µ = 26, Ha: µ < 26, a = 0.05 13)

A) Test statistic: t = -0.87. P- value = 0.8034. Do not reject Ho. There is not sufficient evidence to conclude that the mean is less than 26. The evidence against the null hypothesis is weak or none.

B) Test statistic: t = -0.87. P- value = 0.1966. Do not reject Ho. There is not sufficient evidence to conclude that the mean is less than 26. The evidence against the null hypothesis is weak or none.

Test statistic: t = -0.87. P- value = 0.1922. Do not reject Ho. There is not sufficient evidence to conclude that the mean is less than 26. The evidence against the null hypothesis is weak or none.

D) Test statistic: t = -0.87. P- value = 0.8078. Do not reject Ho. There is not sufficient evidence to conclude that the mean is less than 26. The evidence against the null hypothesis is strong.

Solution:

We are given that:

, s = 9.2, n = 25, Ho: µ = 26, Ha: µ < 26, a = 0.05

We have to choose correct option from given options.

Find t test statistic:

To find the exact p-value, use excel command and Ha: µ < 26 is Left tailed.

So we use following excel command which gives area for left tail or area below t value.

=T.DIST( x , df , cumulative)

where x = t = -0.8696 , df = n - 1 = 25 - 1 = 24 , Cumulative = TRUE

Here we use more decimal places of t to get more accurate answer.

=T.DIST(-0.8696,24,1)

=0.196567

=0.1966

P-value = 0.1966

Thus correct option is B:

B) Test statistic: t = -0.87. P- value = 0.1966. Do not reject Ho. There is not sufficient evidence to conclude that the mean is less than 26. The evidence against the null hypothesis is weak or none.

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