Question

on 6 A sample n.25 is selected from a population with mean, u = 50, 0= 10, a researcher calculated the sample mean, M - 55. Assuming the researcher was performing a two-tailed test, is the sample mean significantly different from the population mean? For the test, a -.05. ed out of Select one: O a.p=0.4938, no difference between the sample mean and the population mean O b.p = 0.0062, significant difference between the sample mean and the population mean O c. p = 0.0124, significant difference between the sample mean and the population mean O d. p = 0.2500, no difference between the sample mean and the population mean.

Answer 1

Ans 6 ) using minitab > stat> one sample z  

we have

One-Sample Z

Test of μ = 50 vs ≠ 50
The assumed standard deviation = 10

N Mean SE Mean 95% CI Z P
25 55.00 2.00 (51.08, 58.92) 2.50 0.0124

option c is true

p = 0.0124, significant difference between sample mean and population mean

Ans 7 ) option b is true

it is known as test statistic

Ans 8 )

using minitab > stat> one sample z  

we have

One-Sample Z

Test of μ = 500 vs < 500
The assumed standard deviation = 15

N Mean SE Mean 95% Bound Z P
25 495.00 3.00 499.93 -1.67 0.048

option b is true

z = 1.67 , p = 0.0475 , accpet the investigator statement

Ans 9 )

One-Sample Z

Test of μ = 70 vs ≠ 70
The assumed standard deviation = 20

N Mean SE Mean 99% CI Z P
36 73.00 3.33 (64.41, 81.59) 0.90 0.368

there is bug in answer because no answer is given as matched

z = 0.9, p = 0.368 ,the sample mean is not significantly different as p >0.01

Ans 10 ) option c is true

the type I error is reject a true H0