Question

Assume that a simple random sample has been selected and test the given claim. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

Listed below are brain volumes in cm3

of unrelated subjects used in a study. Use a 0.05

significance level to test the claim that the population of brain volumes has a mean equal to

1099.2cm3.

962

1027

1273

1080

1070

1174

1068

1347

1101

1205

Answer 1

Solution:

x	x2
962	925444
1027	1054729
1273	1620529
1080	1166400
1070	1144900
1174	1378276
1068	1140624
1347	1814409
1101	1212201
1205	1452025
x=11307	x2=12909537

The sample mean is

Mean   = (x / n) )

= (962+1027+1273+1080+1070,1174+1068+1347+1101+1205 / 10 )

= 11307 / 10

= 11307

Mean   = 1130.7

The sample standard is S

  S = ( x² ) - (( x)² / n ) n -1

= (12909537 ( (155 )² / 10 ) 9

   = (12909537 - 12784824.9 / 9)

= (124712.1 / 9 )

= 13856.9

= 117.7153

The sample standard is 117.71

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :    = 1099.2

H_a :     1099.2

Test statistic = t

= ( - ) / s / n

= (1130.7-1099.2) /117.71 / 10

= 0.846

Test statistic = t =  0.846

P-value =0.4193

= 0.05  

P-value ≥

0.4193 ≥ 0.05

The null hypothesis Ho is not rejected.

Therefore, there is not enough evidence to claim that the population mean μ is different than 1099.2, at the 0.05 significance level