Question

8) A light-bulb manufacturer advertises that the averge life for its light bulbs random sample of 15 of its light bulbs resuted in the following tives in Use Sample Standard Deviatlon hours 995 590 510 530 739 917 571 555 916 728 664 693 708 887 84 test the claim that the sample is from a population with a mean life of 900 hours Use the P.value method of testing Find t Assume that a simple P-value, critical value(s), and pie random sample has been selected from a normally distributed population. state the final conclusion. l est the claim that for the adult population of one town, the mean annual salary is given by u-s 30,000. Sam ple data are summarized as n = 17ふ$22,298, and S-314200 Use a significance level of a 0.05 9)

Answer 1

8) H₀: $\dpi{100} \mu$ = 900

    H₁: $\dpi{100} \mu \neq$ 900

$\dpi{100} \bar x$ = 724.07

s = 156.924

The test statistic t = ($\dpi{100} \bar x - \mu$)/(s/$\dpi{100} \sqrt n$)

                             = (724.07 - 900)/(156.924/$\dpi{100} \sqrt 15$)

                             = -4.342

P-value = 2 * P(T < -4.342)

             = 2 * 0.0003 = 0.0006

Since the P-value is less than the significance level(0.0006 < 0.10), so we should reject the null hypothesis.

At 10% significance level there is not sufficient evidence to support the claim that the sample is from a population with a mean life of 900 hours.

9) H₀: $\dpi{100} \mu$ = 30000

    H₁: $\dpi{100} \mu \neq$ 30000

The test statistic t = ($\dpi{100} \bar x - \mu$)/(s/$\dpi{100} \sqrt n$)

                             = (22298 - 30000)/(14200/$\dpi{100} \sqrt 17$)

                             = -2.236

At alpha = 0.05, the critical values are t_{0.025, 16} = +/- 2.120

Since the test statistic value is less than the critical value (-2.236 < -2.120), so we should reject the null hypothesis.

There is not sufficient evidence to support the claim that the mean salary is $30000.

P-value = 2 * P(T < -2.236)

             = 2 * 0.0200 = 0.04