A study considers if the mean score on a college entrance exam for students in 2005 is any different from the mean score of 501 for students who took the same exam in 1975. Let μ represent the mean score for all students who took the exam in 2005. For a random sample of​ 40,000 students who took the exam in​ 2005, x = 499 and s = 100. (a) Find the test statistic.

Answer:a) z = -4b) p-value 0.00006This result is statistically significant because the p-value is very small, but it is not practically significant because the sample mean of 499 is very close to the null hypothesis mean of 501.Step-by-step explanation:a) The test statistic z is given by [tex]\bf z=\frac{\bar x-\mu}{s/\sqrt{n}}[/tex] where [tex]\bf \bar x[/tex]= 499 the mean for the random sample [tex]\bf \mu[/tex]= 501 the mean in 1975 s = 100 the standard deviation of the sample n = 40,000 the sample size So, [tex]\bf z=\frac{499-501}{100/\sqrt{40,000}}=-4[/tex] b) The p-value would be the area under the Normal N(0,1) outside the interval [-4, 4]. This area equals 0.00006  This result is statistically significant because the p-value is very small, but it is not practically significant because the sample mean of 499 is very close to the null hypothesis mean of 501.