A. Random variable X has a binomial distribution, B(36, 0,5). Use the normal app
ID: 3230182 • Letter: A
Question
A. Random variable X has a binomial distribution, B(36, 0,5). Use the normal approximation,
Compute P{13 < X <= 19}. "<=" means less than or equal. Ans. ____________
B. Random variable X has a normal distribution, N(50, 100).
Compute P{X < 40 or X >= 62.5}. ">=" means greater than or equal. Ans. _________
C. Test the claim that the population of Freshman college students has a mean grade point
average greater than 2.00. Sample statistics, include size = 24, mean = 2.35 and
standard deviation = 0.70. Use a type I error = 0.01. Test hypotheses, including the test
statistic, critical value(s), and conclusion.
D. 4 groups, A, B, C, & D, were randomly selected from a normally distributed population.
Test to find these 4 groups' means are all same (Ho:)
____I_____II______III_ IV
13 9 23 16
9 10 25 11
8 5 18 9
Construct ANOVA table below
Sourc3 df SS MS F
Total
Group source
Error
Explanation / Answer
Null hypothesis
Ho:µ = 2.00
Alternative hypothesis
HA: µ1 > 2.00
the test is one tail test
X^bar =2.35
=2.00
=0.70
n= 24
teat statistic t=(X^bar – ) /( /sqrt(n))
=(2.35-2.00) /(0.70/sqrt(24))
=0.35 /0.1429
= 2.4495
df =n-1 =24-1 =23
critical value z/2 =(z0.005 ) =2.807)
pvalue =1-P(z>2.807)
=1-0.9975
=0.0025
p value < 0.01, accept the Ho
ANOVA table follows
The f-ratio value is 11.6. The p-value is .00277. The result is significant at p < .05.
Summary of Data Treatments 1 2 3 4 5 Total N 3 3 3 3 12 X 30 24 66 36 156 Mean 10 8 22 12 13 X2 314 206 1478 458 2456 Std.Dev. 2.6458 2.6458 3.6056 3.6056 6.2377Related Questions
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