Question

Find the p -value for the hypothesis test. A random sample of size 51 is taken. The sample has a mean of 423 and a standard deviation of 84. H 0 : µ = 400 H a : µ ≠ 400 The p -value for the hypothesis test is . Your answer should be rounded to 4 decimal places.

Answer 1

Given
Hypothesied Mean :	400
Sample Mean :	423
Sample Standard Deviation : s	84
Sample Size : n	51

Degrees of freedom : n-1 = 51-1 = 50

Two tailed test

For Two tailed test

p-value = 0.0562

For finding p-value excel function T.DIST.RT is being used.

T.DIST.RT function
Returns the right-tailed Student's t-distribution.
The t-distribution is used in the hypothesis testing of small sample data sets. Use this function in place of a table of critical values for the t-distribution.
Syntax
T.DIST.RT(x,deg_freedom)
The T.DIST.RT function syntax has the following arguments:
• X Required. The numeric value at which to evaluate the distribution.
• Deg_freedom Required. An integer indicating the number of degrees of freedom.