Question

Question 7 (1 point) Questions 6-10 is one hypothesis testing problem using an Excel data called vacation. We want to know if there is a difference between the average individual vacation budget of this year and that of last year. We collected two independent samples of 15 individuals vacation from each year. We assume population variances are unequal. You already downloaded the data file in Question 6, so you do not have to open it again. Just run a correct tool in the Excel file. but if you want to open it again, click the Excel data file name above. What is the t test statistic? a) 2.29 Ob) 1.72 Oc) 21 O d) 2.07 Question 8 (1 point) Questions 6-10 is one hypothesis testing problem using an Excel data called vacation. We want to know if there is a difference between the average individual vacation budget of this year and that of last year. We collected two independent samples of 15 individuals vacation from each year. We assume population variances are unequal. You already downloaded the data file in Question 6, so you do not have to open it again. Just run a correct tool in the Excel file. but if you want to open it again, click the Excel data file name above. What are critical values? a) +2.08 b) +2.29 Oc) +1.72 d) +0.03

Answer 1

ans Q7) :

Last year	This year
1123	960
954	400
2500	850
1200	750
900	720
900	600
2134	1300
590	650
800	500
1200	0
460	2100
750	800
1900	1000
2400	1000
3740	840

from the given data we calculate sample means and sample standard deviation

$\small \bar{X}$1 =1436.73

$\small \bar{X}$2 = 831.33

s1=911.51

s2 = 462.63

n1= 15

n2=15

Claim that there is difference between the average individual vacation budget of this year and that of last year

and here we assume that population variance are unequal

Let $\small \mu$ 1 : Average individual vacation budget of this year

$\small \mu$2 : Average individual vacation budget that of last year

Test of Hypothesis :

To Test :

H0 :µ1- µ2 versus H1 : µ1 $\small \neq$ µ2  

Test Statistic

X1 X2 t= s12 n1 + s22 n2

1436.73 – 831.33 t= 911.512 15 + 462.632 15

t = 2.29

Ans : The test statistic is t = 2.29

a) 2.29

Ans Q.8)

Claim that there is difference between the average individual vacation budget of this year and that of last year

and here we assume that population variance are unequal

Let $\small \mu$ 1 : Average individual vacation budget of this year

$\small \mu$2 : Average individual vacation budget that of last year

Test of Hypothesis :

To Test :

H0 :µ1- µ2 versus H1 : µ1 $\small \neq$ µ2  

here we have to use two tailed t test for the difference between population mean

Now to calculate  the critical value

given that $\small \alpha$ = 0.05

df = 20.76

then critical value = t_20.76,0.05 = 2.081

Critical region is If | t | > t_20.76,0.05 then reject null hypothesis

critical value = 2.08

Ans : critical value = $\small \pm$ 2.08

a) $\small \pm$ 2.08