Answer:
There is sufficient evidence to conclude that six inches spacing has a higher mean failure pressure than 8 inches
Reject [tex]H_0\ at\ 5%[/tex] level of significance
Step-by-step explanation:
From the question we are told that:
Sample size 1 [tex]n_1=15[/tex]
Spacing 1 [tex]s_1=8[/tex]
Mean 1 [tex]\=x_1=8.48[/tex]
Standard deviation 1 [tex]\sigma_1=0.96 kPa[/tex]
Sample size 2 [tex]n_2=16[/tex]
Spacing 2 [tex]s_2=6[/tex]
Mean 1 [tex]\=x_1=9.93[/tex]
Standard deviation 1[tex]\sigma_1=1.02 kPa[/tex]
Generally the hypothesis is mathematically given as
Null [tex]H_0:\mu_1-\mu_2[/tex]
Alternative [tex]H_a:\mu_1\mu_2[/tex]
Generally the equation for pooled estimate is mathematically given by
[tex]S=\sqrt{\frac{(n_1-1)\sigma_1^2+(n_2-1)\sigma_2^2}{n_1+n_2-2} }[/tex]
Therefore
[tex]S=\sqrt{\frac{(15-1)0.96^2+(16-1)1.02^2}{15+15-2} }[/tex]
[tex]S=0.9905[/tex]
Generally the equation for test statistics is mathematically given by
[tex]t=\frac{\=x_1+\=x_2}{S\sqrt{\frac{1}{n _1}+\frac{1}{n_2}}}[/tex]
[tex]t=\frac{\=8.48-9.93}{0.9905\sqrt{\frac{1}{15}+\frac{1}{15}}}[/tex]
[tex]t=-4.00091[/tex]
Therefore From table
[tex]P value=P(t_{15+15-2}=4.00091)[/tex]
[tex]P value=0.00041918[/tex]
[tex]P<0.0005[/tex]
Therefore
There is sufficient evidence to conclude that six inches spacing has a higher mean failure pressure than 8 inches
Reject [tex]H_0\ at\ 5%[/tex] level of significance
