Business statistics

Question

You wish to test the following claim (HaHa) at a significance level of α=0.005α=0.005.

      Ho:μ=55.5Ho:μ=55.5 

      Ha:μ≠55.5Ha:μ≠55.5

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=8n=8 with mean M=65.5M=65.5 and a standard deviation of SD=14.1SD=14.1.

What is the p-value for this sample? (Report answer accurate to four decimal places.) 

p-value = 

Answer 1

Hi Salma,

Given that we don't know a population standard deviation, we have to use t rather than z. Test statistic is:

t=x-bar-mu/SE

Breaking this down:

x-bar=sample mean

mu=popularion mean

SE=standard error, which has its own formula

SE=s/sqrt (n)

s=sample standard deviation

n=sample size

Now, for our sample:

s=14.1

n=8

SE=14.1/sqrt(8)

SE=4.986

Now, returning to the original formula:

t=(x-bar-mu)/SE

x-bar=65.5

mu=55.5

SE=4.986

t=(65.5-55.5)/4.986

t=2.005

Now, let's talk about degrees of freedom (df)

df=n-1

n=sample size=8

df=8-1

df=7

So, go to the t-table, look at the row for 7 degrees of freedom, and find the test statistic 2.005. It falls between 1.895 and 2.365, which corresponds, for two-sided tests, to p-values of 0.10 and 0.05 respectively. Therefore:

0.0500 < p < 0.1000

We cannot get any closer estimate of p-value without using statistical software. I hope this helps.