Question

11) Is there a significant difference at a = 0.10 in the average heights in feet of high towers in Europe and the ones in South Africa? The data are shown. 497 463 888 Europe 1236 1288 1312 987 365 South Africa 714 705 964 1227 325 830 369 721 1799

Answer 1

Here we want to test whether there is a significant difference in the average heights in feet of high towers in Europe and South Africa.

Let  
11
   be the average heights in feet of high towers in Europe and let  
112
  be the average heights in feet of high towers in South Africa.

The null hypothesis is given as

Ho: M1 = 42

i.e   there is no  significant difference in the average heights in feet of high towers in Europe and South Africa

$H_{1} : \mu_{1} \mp\mu_{2}$

i.e there is a significant difference in the average heights in feet of high towers in Europe and South Africa.

Let x be the sample  heights in feet of high towers in Europe is

497 463 888 1236 1312 365 1288 987

Let y be sample heights in feet of high towers in South Africa.

714 1227 369 705 325 721 964 830 1799

Sample sizes is given as

n1 = 8

n2 = 9

The sample mean is given as

C n1

7036 8

= 879.5

3 : Σ9 η2

7654 9

= 850.4444

Calculating variance

si - n1*.72 nl - 1

=  153876.9

Calculating variance

2 S2 Σy – n2 * y? n2 – 1

= 202409

The pooled variance will be ( assuming equal variances  )

$2 nl* si + n2 * sź nl + n2 - 2

$=\frac{8* 153876.9 +9* 202409}{8+9-2}$

$=\frac{ 3052696}{8+9-2}$

= 203513.1

Test statistic is

tni+n2-2 T-Y V1/n1 + 1/n2 S*

$=\frac{ 879.5 - 850.4444 }{451.1243 * \sqrt{1 /8 + 1/9} }$

$=\frac{ 29.05556 }{451.1243 * 0.4859127 }$

$=\frac{ 29.05556 }{219.207 }$

= 0.1325485

The p-value with degree of freedom

df = n1 + n2 -1

= 8 + 9 -2

= 15

The p-value is given as

$P[\left |t_{n_{1}+n_{2}-2} \right | >0.1325485 ] = 0.8963122$

At 0.10 level of significance

p-value = 0.8963 > 0.10

Failed to reject the null hypothesis .

There is no sufficient evidence that there a significant difference in the average heights in feet of high towers in Europe and South Africa .