Question

what is the critical value.

Are you smarter than a second-grader? A random sample of 62 second-graders in a certain school district are given a standardized mathematics skills test. The sample mean score is x = 56. Assume the standard deviation of test scores is o= 16. The nationwide average score on this test is 52. The school superintendent wants to know whether the second-graders in her school district have greater math skills than the nationwide average. Use the a=0.05 level of significance and the critical value method. Part 1 of 5 (a) State the appropriate null and alternate hypotheses H: = 52 H, H > 52 This hypothesis test is a lot Part: 1/5 Part 2 of 5 Find the critical value(s). Round the answer(s) to three decimal places, if necessary. If there is more than one critical value, separate them with commas. Critical value(s): 1

Answer 1

Answer: 1) In order to test the given claim, we construct the null and alternative hypotheses as H0: mu = 52 vs Ha: mu > 52

where mu is the unknown population mean score of mathematics skill test. This hypothesis test is a right-tailed test.

2) The test statistic for the given problem is Z = (xbar - mu0)/(sigma/sqrt(n)),

where xbar = sample mean, mu0 = the hypothesized value of the population mean, n = sample size, s = sample standard deviation, sqrt refers to the square root function. Under H0, Z ~ N(0,1) [It follows Normal distribution since we are given the assumed population standard deviation]

We reject H0 if Z(observed) > tau(alpha), where tau(alpha) is the upper alpha point of the Standard Normal Distribution. This is known as the critical value for the given test. alpha = level of significance.

Here, Z(observed) = 1.968502 and tau(alpha) =   1.670 (rounded to three decimals) (Obtained from the probability table of Standard Normal Distribution)

So, critical value = 1.670.
Hence,Z(observed) > tau(alpha).

So we reject H0 and conclude at a 5% level of significance on the basis of the given sample measures that there is enough evidence to say that the second graders in her school district have greater mathematics skills than nationwide average.