Question

Test the claim about the population mean μ at the level of significance α. Assume the population is normally distributed.

Claim: μ ≠ 33; α = 0.05; σ = 2.7
Sample statistics:   = 32.1, n = 35

Answer 1

Let our sample be  .

Since, the population is normally distributed, we have:

for  

Since, 's are i.i.d, we have:

where,   is the sample mean

In our case, the population mean   is unknown and we want to test the claim that  .

It is also given that,  ,   , and the level of significance in the testing of the claim is

Now,

Now, if we try to find the   Confidence Interval for the population mean  , then it can be done as follows:

   is denoted as the th percentile of the distribution

and since,    

Since, for distribution,    

In our case, by looking at the - table, we get the th percentile as:

After putting all the corresponding values in the above inequality, we get,

Hence, we have found that the   Confidence Interval for the population mean   is

and clearly,   

Hence, if we had made the claim of  , then it would have got rejected for the level of significance  

Therefore, our claim that   is justified i.e. the claim   does not get rejected. (Ans.)