Question

(V) A type II error occurs when our estimate for the mean discharge temperature is lower than the actual temperature. Q. No. 10. Lightbulbs of a certain type are advertised as having an average lifetime of 750 hours. The price of these bulbs is very favorable, so a potential customer has decided to go ahead with a purchase arrangement unless it can be conclusively demonstrated that the true average lifetime is smaller than what is advertised. A random sample of 45 bulbs was selected, the lifetime of each bulb determined, and the appropriate hypotheses were tested using MINITAB, resulting in the accompanying output. Variable N Lifetime 4 Mean St Dev St errorZ 738.4437.58 5.60 2.06 0.020 What conclusion would be appropriate for a significance level of 0.057 (I) Do not reject the null hypothesis. There is sufficient evidence to conclude that the (II) Reject the null hypothesis. There is not sufficient evidence to conclude that the (III) Do not reject the null hypothesis. There is not sufficient evidence to conclude that (IV) Reject the null hypothesis. There is sufficlent evidence to conclude that the lifetime of a bulb is less than 750 hours. lifetime of a bulb is less than 750 hours. the lifetime of a bulb is less than 750 hours. lifetime of a bulb is less than 750 hours. Q. No. 11. A statistical program is recommended. Have you ever been frustrated because you could not get a container of some sort to release the last bit of its contents? An article reported on an investigation of this issue for various consumer products. Suppose five 6.0 oz tubes of toothpaste of a particular brand are randomly selected and squeezed until no more toothpaste will come out. Then each tube is cut open and the amount remaining is weighed, resulting in the following data: 0.53,0.64, 0.42, 0.5, 0.35 roUOO(0 11h@???? 120 (a) ( ) ?@ Mark Reflex EM-17567-4:14

Answer 1

Solution ( 10 ) :

   We are given that following results regaring the test of hypothesis that average lifetime of lightbulbs of certain type is 750 or less than 750 hours.

Variable	N	Mean	Sd Dev	St Error	Z	p-value
Lifetime	45	738.44	37.58	5.6	-2.06	0.02

we have to make correct conclusion at 0.05 level of significance.

State H0 and H1:

$H_{0}:\mu=750\: \: \: \: \: Vs\: \: \: \: \: H_{1}:\mu<750$

Decision rule : We reject H0 , if p value < 0.05 level of significance
otherwise we fail to reject H0.

since p value = 0.020 < 0.05 level of significance , we reject null hypothesis H0.

Thus there is sufficient evidence to to conclude that the lifetime of a bulb is less than 750 hours.

Thus correct option is :

IV) Reject null hypothesis H0. There is sufficient evidence to to conclude that the lifetime of a bulb is less than 750 hours.