The average number of pages for a simple random sample of 40 physics textbooks is 435. The average number of pages for a simple random sample of 40 mathematics textbooks is 410. Assume that all page length for each types of textbooks is normally distributed. The standard deviation of page length for all physics textbooks is known to be 100, and the standard deviation of page length for all mathematics textbooks is known to be 100.Assuming that on average, mathematics textbooks and physics textbooks have the same number of pages, what is the probability of picking samples of these sizes and getting a sample mean so much higher for the physics textbooks (one-sided p-value, to four places)?

Answer:Step-by-step explanation:Let x be denoting physics text books and y mathematics text booksMean 435.00 410.00 SD 100.00 100.00 SEM 15.81 15.81 N 40     40     (SEM is calculated as std deviation/square root of (n))[tex]\bar x -\bar y = 25[/tex]Std error for difference = 22.361Degree of freedom = n1+n2-2=[tex]40+40-2 =78[/tex]test statistic t = mean difference/std error = [tex]\frac{25}{22.361} =1.180[/tex][tex]H_0: \ bar x = \bar y\\H_a: \bar x > \bar Y[/tex](Right tailed test at 5% significance level)p value = 0.2670Since p value >0.05, our alpha we accept null hypothesis.the probability of picking samples of these sizes and getting a sample mean so much higher for the physics textbooks (one-sided p-value, to four places)=0.2670