Question

provided below are summary statistics for independent simple random samples from two populations. use the pooled t - test and the pooled t - interval procedure to conduct the required hypothesis test and obtain the specified confidence interval.
\\( \overline { x } _ { 1 } = 10, s _ { 1 } = 2.1, n _ { 1 } = 13, \overline { x } _ { 2 } = 12, s _ { 2 } = 2.1, n _ { 2 } = 13 \\)
a. two - tailed test, \\( \alpha = 0.01 \\)
b. \\( 99 \\% \\) confidence interval
a. first, what are the correct hypotheses for a two - tailed test?
\\( \bigcirc \\) a. \\( h _ { 0 } : \mu _ { 1 } < \mu _ { 2 } \\)
\\( h _ { a } : \mu _ { 1 } = \mu _ { 2 } \\)
\\( \bigcirc \\) c. \\( h _ { 0 } : \mu _ { 1 } = \mu _ { 2 } \\)
\\( h _ { a } : \mu _ { 1 } \
eq \mu _ { 2 } \\)
\\( \bigcirc \\) e. \\( h _ { 0 } : \mu _ { 1 } > \mu _ { 2 } \\)
\\( h _ { a } : \mu _ { 1 } = \mu _ { 2 } \\)
\\( \bigcirc \\) b. \\( h _ { 0 } : \mu _ { 1 } \
eq \mu _ { 2 } \\)
\\( h _ { a } : \mu _ { 1 } = \mu _ { 2 } \\)
\\( \bigcirc \\) d. \\( h _ { 0 } : \mu _ { 1 } = \mu _ { 2 } \\)
\\( h _ { a } : \mu _ { 1 } > \mu _ { 2 } \\)
\\( \bigcirc \\) f. \\( h _ { 0 } : \mu _ { 1 } = \mu _ { 2 } \\)
\\( h _ { a } : \mu _ { 1 } < \mu _ { 2 } \\)

Explanation:

In a two - tailed test, the null hypothesis \(H_0\) assumes no difference between the population means (\(\mu_1=\mu_2\)), and the alternative hypothesis \(H_a\) assumes a difference (\(\mu_1
eq\mu_2\)).

Answer:

C. \(H_0:\mu_1 = \mu_2\), \(H_a:\mu_1
eq\mu_2\)