Question

Testing a claim about a population mean: t-Test

You work for a steel company that produces "lag bolts". One product is a 10-inch lag bolt. A recent re-design of a machine involved in the production of these bolts has the company wondering whether the production still produces 10-inch lag bolts. You have gathered a random sample of bolts that have been produced with this new production process. Conduct an appropriate test, at a 5% significance level (tα/2=t0.025≈2.1314)(tα/2=t0.025≈2.1314), to determine if the overall mean for this process is 10 inches.

Data (lag bolt lengths, measured in inches):

9.97	9.93	10.02	9.97	10.06	9.95	10.04	9.93
10.00	10.02	10.10	10.02	9.98	9.96	10.01	9.98

Sample Statistics

n=16

¯x=9.99625

s=0.04674

Carry out the procedure ("crunch the numbers"):

1. Sample mean: x¯≈
2. Standard error of the sample mean: σx¯≈
3. Standardized test statistic: t≈
4. P-value:

Answer 1

null hypothesis: HO: μ		=	10
Alternate Hypothesis: Ha: μ		≠	10

a)

from excel:

sample mean =average(Array) =9.99625

b)

sample size    n=		16
std deviation s=		0.0467
std error ='sx=s/√n=0.04674/√16=		0.01169

c)

test statistic t ='(x̄-μ)/sx=(9.99625-10)/0.012=

-0.3209

d)

p value      =

0.7527

from excel: tdist(0.321,15,2)

since p value is greater than level of significance, we fail to reject null hypothesis