Question

Question 10: Perform a z-test to determine if the mean age is different than 60 years. (13 pts.)
	Data
	Null Hypothesis				60.0
	Level of Significance				0.05
	Population Standard Deviation				5.0767272
	Sample Size				101
	Sample Mean				56.29703
	Intermediate Calculations
	Standard Error of the Mean				0.5052
	Z Test Statistic
	Two-Tail Test
	Lower Critical Value
	Upper Critical Value
	p-Value

Please use excel and explain clearly with the formula used. I cannot put the data as it is too long but for your information, I have 101 data of one column. Use any data you want.

Answer 1

Data
Null Hypothesis		60
Level of significance		0.05
Population Standard Deviation		5.0767272
Sample Size		101
sample Mean		56.29703

Intermediate Calculation			Formula Used
Standard Error of the mean		0.5052	= 5.0767272/SQRT(101)
Z test Statistic		-7.32971101	= (56.29703- 60)/0.5052

Two tail Test			Formula Used
Lower Critical Value		-1.95996398	= NORMINV(0.025,0,1)
Upper Critical Value		1.959963985	= NORMINV(1-0.025,0,1)
p value		2.3065E-13	= 2*NORMDIST(-7.3297,0,1,1)

Last Column is formula used

(For p value we should multiply it by 2 as it is two tailed so we need to find p(z<-7.3297) and p(z> +7.3297) so due to symmetry of normal distribution, multiplication of 2 is valid)