Question

A sample mean, sample size, and population standard deviation are given. Use the one-mean z-test to perform the required hypothesis test at the given significance level. Use the critical -value approach. 20) -7.1, n = 18,0 = 1.5, Ho: u = 10; Ha: < 10, a = 0.01 A) z = -8.20; critical value=-2.33; reject Ho B) Z -8.20; critical value = 1.96; do not reject Ho C) Z=-8.20; critical value = -2.33; do not reject Ho D) 2 --8.20; critical value = -1.96; reject Ho

Answer 1

ANSWER:

Given that

Sample mean  x bar =7.1

Sample size (n) = 18

standard deviation ( $\tiny \sigma$ ) =1.5

Null hypothesis (H₀) = $\tiny \mu$ =10

Alternative hypothesis (H₁) = $\tiny \mu$ $\tiny \neq$ 10

Test statistic Z= (x bar - $\tiny \mu$ ) / ( $\tiny \sigma$ /$\tiny \sqrt{}$n)

= (7.1-10) / (1.5 / $\tiny \sqrt{}$ 18)

= -2.9 / 0.3535

  Z = -8.20

critical value = (x bar - $\tiny \mu$ ) /  $\tiny \sigma$

= (7.1-10) / (1.5) = -2.9 / 1.5

critical value = -1.93 $\tiny \approx$ -1.96

option D ; Reject H₀.