A random sample of 80 eighth grade students\' scores on a national mathematics a

Question

A random sample of 80 eighth grade students' scores on a national mathematics assessment test has a mean score of 277. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 270. Assume that the population standard deviation is 31. At alpha = 0.06, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). (a) Write the claim mathematically and identify H_0 and H_a. Choose the correct answer below. A. H_0: mu lessthanorequalto 270 (claim) H_a: mu > 270 B. H_0: mu = 270 (claim) H_a: mu > 270 C. H_0: mu greaterthanorequalto 270 (claim) H_a: mu 270 (claim) E. H_0: mu = 270 H_a: mu > 270 (claim) F. H_0: mu

Explanation / Answer

Given that,
population mean(u)=270
standard deviation, s =31
sample mean, x =277
number (n)=80
null, Ho: µ=270
alternate, H1: µ>270
level of significance, a = 0.06
from standard normal table,right tailed z a/2 =1.555
since our test is right-tailed
reject Ho, if zo > 1.555
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 277-270/(31/sqrt(80)
zo = 2.01967
| zo | = 2.01967
critical value
the value of |z a| at los 6% is 1.555
we got |zo| =2.01967 & | z a | = 1.555
make decision
hence value of | zo | > | z a| and here we reject Ho
p-value : right tail - ha : ( p > 2.01967 ) = 0.02171
hence value of p0.06 > 0.02171, here we reject Hoa

ANSWERS
---------------
null, Ho: µ=270
alternate, H1: µ>270
test statistic: 2.01967
critical value: 1.555
decision: reject Ho
p-value: 0.02171

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