When bonding teeth, orthodontists must maintain a dry field A new bonding adhesi

Question

When bonding teeth, orthodontists must maintain a dry field A new bonding adhesive has been developed to eliminate the necessity of a dry field However there is concem that the new bonding adhesive is not as strong as the current standard a composite adhesive Tests on a sample of 10.xtracted toethbonded with the new adhesive resulted in a mean breaking strength later 24 hours) ofx 497 Mpa and a standard deviation of 0.45 Mpa orthodontists want to knowifthe tue mean breaking strengh is less than 545 Mpa the man breaking strength of the composite adhesive. a. Set up the mul and altemative hypotheses for the test Choose the comect answer below O A. H.: w2545 vs H, 545 O B. Ho: H 545 vs. Ha: w 5.45 O D. Ho: u 545 vs. Ha: 545 O F. Ho: 497 vs. Ha: 497 b. Find the rejection region for the test using as 0.05 Choose the comect answer below 1833 O B. t -1.833 O t

Explanation / Answer

a) answer e

H0: mu = 5.45

H1: mu <=5.45

The null hypothesis is mean to be 5.45 or above, but in null hypothesis we don't add inequality

we want to check if the observed mean is less than 5.45 or not, hence the alternate hypothesis is mu <=5.45

b) t value at 0.05 = -1.83

t value at 0.04 = -1.97

answer a) t < -1.83 is the rejection region at 0.05

c) t stat = (4.97-5.45) / (0.45/sqrt(10)) = 3.73

d) answer d)

There is sufficient evidence to indicate mu < 5.45

e) answer a

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