A random sample of 8 buckets of cement had a mean of 105625

A random sample of 8 buckets of cement had a mean of 105.625 lbs with a standard deviation of 21.62. Based on the sample, perform a hypothesis test to test the claim that the mean of the sample is greater than 100lbs at a=.05

Find

a. h0

b. ha

c. u

d. x-

e. Sx

f. critical value of t

g. p - value

h. t statistic =

i. reject or fail to reject h0

j. explain your decision

Solution

Here we are given that,

number of buckets of cement (n) = 8

Sample mean (Xbar) = 105.625

sample standard deviation (sd) = 21.62

Here the test of the hypothesis is,

H0 : mu = 100 Vs H1 : mu > 100

where mu is the population mean.

We can find critical value of t using EXCEL.

syntax :

tinv(probability, d.f)

where probability = alpha

d.f =n-1 = 8-1 = 7

critical value = 2.3646

P-value syntax in EXCEL:

=tdist(x,d.f., tails)

where x is thetest statistic value

d.f.=n-1

tails = 1

P-value = 0.2429

P-value > alpha(a)

Accept H0(fail to reject H0) at 5% level of significance.

Conclusion : the mean of the sample is 100lbs .