Question

10.36 A consumer testing organization wants to know whether two brands of work shoes have equally long-lasting heels. Tests show that 50 randomly selected workers wore out the heels of Brand X shoes, on average, in 96 days with a standard deviation of 6.4 days, while 50 randomly selected workers wore out the heels of Brand Y shoes, on average, in 99 days with a standard deviation of 6.1 days. (a) Test at the level of significance a = 0.05 whether the difference between the two average wearing lives is significant. (b) Compute the p-value and use it to decide whether the difference between the sample means is significant at the 0.05 level of significance.

Answer 1

Given that:

  Tests show that 50 randomly selected workers wore out the heels of Brand X shoes,

  on average, in 96 days with a standard deviation of 6.4 days

  while 50 randomly selected workers wore out the heels of Brand Y shoes, on average, in 99 days with a standard deviation of 6.1 days.

find:

a. Test at the level of significance α=0.05α=0.05 whether the difference between the two average wearing lives is significant.

b. Compute the p-value and use it to decide whether the difference between the sample means is significant at the 0.05 level of significance.

Answere set up hypothelis Null, HO: 01242 alternate , difference is significant uliuli=U2 Test statista xi mean) = 96. standard devictions.d1 )=6.49 Numberinile 50 - Ylmean)=99 Standard deviations (s. 12) =615 Member (12) 250 we use text Statistů 14) =(x-4) HCs.dino) teschi ymu to = 96-99/JC40.96150)+(34.21750) tor- 11018192) +(0.7442) to = = W 1:5634 to 1 25035

to = -2.399 Hol.-8.399. Colitical vallle- The value of tal- with min (n1-1, 02-1) se uadt is 2.01 we got toli=9,3993) Ital = 2:01 Hence value of Hol > Ital and here we reject the P-value two failed (double the one tecil) - Ha = (p! =-2.3993) = 0.02 tence value of poros 20.02 > 0.02 Heute Reject to 9, The level of significant 220.05 whether the dibb blw two ang wearing lives is significant is dobbeogjent is signibreant' P20.02 Plo. 0770.02) we steject to