Question

are you smarter than a second - grader? a random sample of 61 second - graders in a certain school district are given a standardized mathematics skills test. the sample mean score is \\(\bar{x} = 51\\). assume the standard deviation of test scores is \\(\sigma = 10\\). the nationwide average score on this test is 54. the school superintendent wants to know whether the second - graders in her school district have different math skills than the nationwide average. use the \\(\alpha = 0.01\\) level of significance and the p - value method with excel.\
part: 0 / 5\
part 1 of 5\
(a) state the appropriate null and alternate hypotheses.\
\\(h_0:\mu = 54\\)\
\\(h_1:\mu\
eq54\\)\
this hypothesis test is a \\(\boxed{\text{select}}\\) test.\
(options: left - tailed, right - tailed, two - tailed)

Explanation:

Step1: Analyze the alternative hypothesis

The alternative hypothesis \( H_1: \mu
eq 54 \) indicates that we are testing for a difference in either direction (less than or greater than the hypothesized mean of 54).

Step2: Determine the test type

A two - tailed test is used when the alternative hypothesis has a "not equal to" (\(
eq \)) sign, as it considers both tails of the distribution (values significantly less than 54 and significantly greater than 54). A left - tailed test would have \( H_1:\mu < 54 \) and a right - tailed test would have \( H_1:\mu>54 \), which is not the case here.

Answer:

two - tailed