Question

are you smarter than a second grader? a random sample of 45 second graders in a certain school district are given a standardized mathematics skills test. the sample mean score is \\( \bar{x} = 54 \\). assume the standard deviation of test scores is \\( \sigma = 15 \\). the nationwide average score on this test is 50. 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 = 0.05 \\) level of significance and the \\( p \\)-value method with the ti-84 plus calculator. \
part: 0 / 5 \
part 1 of 5 \
(a) state the appropriate null and alternate hypotheses. \
\\( h_0: \\) \\( \square \\) \
\\( h_1: \\) \\( \square \\) \
this hypothesis test is a \\( \boxed{\text{select}} \\) test. \
there is a button panel with symbols like \\( \
eq \\), \\( \mu \\), \\( < \\), \\( > \\), \\( = \\), and buttons for refresh and close.

Explanation:

Step1: Define Null Hypothesis

The null hypothesis \( H_0 \) assumes no difference, so \( H_0: \mu = 50 \) (where \( \mu \) is the population mean of second - graders' scores, and 50 is the nationwide average).

Step2: Define Alternative Hypothesis

The superintendent wants to know if scores are different, so it's a two - tailed test. Thus, \( H_1: \mu
eq 50 \). Also, this is a z - test (since population standard deviation \( \sigma = 15 \) is known) or a one - sample z - test for mean, but in terms of the test type (two - tailed as we are testing for "different" from the nationwide average).

Answer:

\( H_0: \boldsymbol{\mu = 50} \), \( H_1: \boldsymbol{\mu
eq 50} \), and this is a two - tailed test.