a)
Sample size = (Z/2
*
/ E)2
= ( 1.6449 * 47 / 5 )2
= 239.08
Sample size = 240 (Rounded up to nearest integer)
b)
The null and alternative hypothesis are
H0:
>= 247
Ha:
< 247
c)
From Z table,
Critical value Z/2
= Z0.10/2 = Z0.05 =
1.6449
d)
Test statistics
z = (
-
) / (
/ sqrt (n) )
= ( 237 - 247 ) / (47 / sqrt ( 30) )
= -1.17
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