Answer:
a) Alternative hypothesis, [tex]H_{a} : \mu_{1} \neq \mu_{2}[/tex]
b) z = -2.91, Pvalue = 0.002
c)Option C. Reject H_0. There is enough evidence at the 1% level of significance to reject the claim.
Step-by-step explanation:
a) Null hypothesis, [tex]H_{0} : \mu_{1} = \mu_{2}[/tex]
Alternative hypothesis, [tex]H_{a} : \mu_{1} \neq \mu_{2}[/tex]
b) Standardized test statistic
Level of significance, [tex]\alpha = 0.01[/tex]
[tex]\sigma_{1} = 3.2[/tex]
[tex]\sigma_{2} = 1.7[/tex]
[tex]X_{1} = 16\\X_{2} = 18\\n_{1} = 30\\n_{2} = 27[/tex]
[tex]z = \frac{\mu_{1}- \mu_{2} }{\sqrt{\frac{\sigma_{1} ^{2} }{n_{1} } + \frac{\sigma_{2} ^{2} }{n_{2} } }}[/tex]
[tex]z = \frac{16-18 }{\sqrt{\frac{3.2^{2} }{30 } + \frac{1.7 ^{2} }{27 } }}[/tex]
z = -2.91
Checking the p-value that corresponds to z = -2.906
P-value = 0.002
c) What is the proper decision
P-value = 0.002
Level of significance, α = 0.01
0.002 < 0.01
Since Pvalue < α, the null hypothesis H₀ should be rejected.
Option C is the correct option.
