A recent study was conducted to determine the curing efficiency (time to harden) of dental composites (resins for the restoration of damaged teeth) using two different types of lights. Independent random samples of lights were obtained and a certain composite was cured for 40 seconds. The depth of each cure (in mm) was measured using a penetrometer. The summary statistics for the Halogen light were n_1 = 10, x_1 = 5.35, and s_1 = 0.7. The summary statistics for the LuxOMax light were n_2 = 10, x_2 = 3.90, and s_2 = 0.8. Assume the underlying populations are normal, with equal variances. a. The maker of the Halogen light claims that they produce a larger cure depth after 40 seconds than LuxOMax lights. Is there any evidence to support this claim? Use alpha = 0.01. b. Construct a 99% confidence interval for the difference in population mean cure depths.

Answer:(1.4328, 1.622)Claim is supported by evidence.Step-by-step explanation:Given that a  recent study was conducted to determine the curing efficiency (time to harden) of dental composites (resins for the restoration of damaged teeth) using two different types of lights. Let X be the halogen and y the Luxomax light[tex]H_0: \bar x =\bar y\\H_a: \bar x > \bar Y[/tex](Two tailed test)we are given data as: Group   Group One     Group Two   Mean   5.3500            3.9000 SD             0.7000     0.8000 SEM       0.2214     0.2530 N                10                 10       The mean of Group One minus Group Two equals 1.4500Std error for difference =  0.336Test statistic t=4.3135  df = 18p value = 0.0004Since p <0.01 at 1% level, reject H0There is significant difference and hence the claim is valid.There  is evidence to support this claim at 1% significance levelMargin of error =1.17299% confidence interval = [tex](1.45-1.172, 1.45+1.172)\\\\=(1.4328, 1.622)[/tex]