Answer:
The null hypothesis is [tex]H_o: \mu_1 = \mu_2[/tex]
The alternative hypothesis is [tex]H_1 : \mu_1 \ne \mu_2[/tex]
The test statistics is [tex]t = -1.667[/tex]
Step-by-step explanation:
From the question we are told that
The first sample size is [tex]n_1 = 12[/tex]
The first sample mean is [tex]\= x_1 = 79.8[/tex]
The first standard deviation is [tex]\sigma _1 = 8.8[/tex]
The second sample size is [tex]n_2 = 17[/tex]
The second sample mean is [tex]\= x_2 = 85.2[/tex]
The second standard deviation is [tex]\sigma _2 = 8.3[/tex]
The null hypothesis is [tex]H_o: \mu_1 = \mu_2[/tex]
The alternative hypothesis is [tex]H_1 : \mu_1 \ne \mu_2[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x_ 1 - \= x_2 }{ \sqrt{ \frac{\sigma_1^2 }{n_1 } +\frac{\sigma_2^2 }{n_2} } }[/tex]
=> [tex]t = \frac{ 79.8 - 85.2 }{ \sqrt{ \frac{8.8^2 }{12} +\frac{ 8.3^2 }{17} } }[/tex]
=> [tex]t = -1.667[/tex]
