Homework Sourse7 A random sample of 8989 eighth grade students scores on a
7-
A random sample of
8989
eighth grade students\' scores on a national mathematics assessment test has a mean score of
288288.
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
280280.
Assume that the population standard deviation is
3030.
At
alphaequals=0.050.05,
is there enough evidence to support the administrator\'s claim? Complete parts (a) through (e).
(a) Write the claim mathematically and identify
Upper H 0H0
and
Upper H Subscript aHa.
Choose the correct answer below.
A.
Upper H 0H0:
muequals=280280
Upper H Subscript aHa:
mugreater than>280280
(claim)
B.
Upper H 0H0:
mugreater than or equals280280
(claim)
Upper H Subscript aHa:
muless than<280280
C.
Upper H 0H0:
muless than or equals280280
(claim)
Upper H Subscript aHa:
mugreater than>280280
D.
Upper H 0H0:
muless than or equals280280
Upper H Subscript aHa:
mugreater than>280280
(claim)
E.
Upper H 0H0:
muless than<280280
Upper H Subscript aHa:
mugreater than or equals280280
(claim)
F.
Upper H 0H0:
muequals=280280
(claim)
Upper H Subscript aHa:
mugreater than>280280
(b) Find the standardized test statistic z, and its corresponding area.
zequals=nothing
(Round to two decimal places as needed.)
(c) Find the P-value.
Solution
a)
Formulating the null and alternative hypotheses,
Ho: u <= 280
Ha: u > 280 [ANSWER]
***********************
b)
As we can see, this is a right tailed test.
Getting the test statistic, as
X = sample mean = 288
uo = hypothesized mean = 280
n = sample size = 89
s = standard deviation = 30
Thus, z = (X - uo) * sqrt(n) / s = 2.515728302 [ANSWER]
**********************
c)
Also, the p value is, as this is right tailed,
p = 0.005939336 [ANSWER]
