Question

The accounts of a corporation show that, on average, accounts receivable are $ 275.47. An auditor checked a random sample of 16 of these accounts. The sample mean was $ 270.93 and the sample standard deviation was $ 28.53. Assume that the population distribution is normal. Test the null hypothesis that the population mean is $ 275.47, against a two-sided alternative. Answer the following, rounding your answers to three decimal places where appropriate.

(a) What is the test statistic?  

(b) What is the p-value of the test?  

Answer 1

Given : Sample size=n=16

Sample mean=

X = 270,93

Sample standard deviation=s=28.53

Hypothesized value=

μη = 275.47

Hypothesis :
Η :μ = 275.47
VS  
H, :μά 275.47

Since , the population standard deviation is unknown and sample size is less than 30.

Therefore , use t-test.

(a) The test statistic is ,

X-HO tstat = tn-1

270.93 – 275.47 28.53/16 -=-0.637

(b) p-value = ; from excel "=TDIST(0.637,15,2)"

Ptn-1 > tstat) = P(t16-1 > 0.637) = 0.534