Question

Ihe output voltage of power supply is assumed to be norm random on voltage are as follows: 14.22,13.77,16.85,15.43,14.62 a) Test the hypothesis that the mean voltage equals 15 V against a two-sided alternative hypothesis. Assume α 0.05 Construct a 95% two sided confidence interval on b) 81.03

Answer 1

a)

H0: $\mu$ = 15

Ha: $\mu$$\neq$ 15

From given sample,

$\bar{x}$ = 15.038 , S = 1.2464

Test statistics

t = $\bar{x}$ - $\mu$ / S / sqrt(n)

= 15.038 - 15 / 1.2464 / sqrt(5)

= 0.07

t critical value at 0.05 level with 4 df = $\pm$2.776

Since test statistics falls in non rejection region, we do not have sufficient evidence to reject the null hypothesis.

b)

95% confidence interval for $\mu$ is

$\bar{x}$ - t * S / sqrt(n) < $\mu$ < $\bar{x}$ + t * S / sqrt(n)

15.038 - 2.776 * 1.2464 / sqrt(5) < $\mu$ < 15.038 + 2.776 * 1.2464 / sqrt(5)

13.52 < $\mu$ < 16.59

95% CI is ( 13.52 , 16.59)

Since claimed proportion is lies in confidence interval, we do not have sufficient evidence to reject

the null hypothesis.