Question

Problem 4: In a sample of 1000 Yuba College students, it was found that they consumed on
average 23 grams of sugar with a standard deviation of 4 grams and that 230 planned to transfer
to Chico State.
a) (7 points) Can we conclude with 99% confidence that Yuba College students consume on
average over 20 grams of sugar? Use the rejection region approach.

(7 points) Can we conclude with 99% confidence that under 25% of Yuba College students
plan to transfer to Chico State? Use the p-value approach.

Answer 1

n=1000, =20,

= 23, s= 4, x= 230

a)

c= 99% , =0.01

the null and alternative hypotheses is

Ho: 20
Ha: > 20

Calculte test statistic

t = 23.717

Test statistic: t = 23.717

calculate t critical values for right tailed test with =0.01 and df= n-1 = 1000-1=999

using t table we get

Critical values are = 2.334

decision rule is

Reject Ho if t > 2.334

here (t= 23.717) > 2.334

hence,

Reject the Null hypothesis (Ho).

Conclusion:
There is sufficient evidence to support the claim that the Yuba College students consume on average over 20 grams of sugar at c=99%.

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b)

c=99% , x= 230 , n= 1000, p= 25% =0.25

Ho: P 0.25

Ha: P < 0.25

z =-1.46

Test statistics = 1.46

P-Value = P(z < 1.46)

using normal z table we get

P(z < 1.46) = 0.0721

P-Value = 0.0721

decision rule is

Reject Ho if (P-Value) < ( )

here, (P-Value= 0.0721) > ( = 0.01 )

Hence,

Failed to reject null hypothesis.

conclusion:

Therefore there is NOT sufficient evidece to support the claim that the proportion of Yuba College students who plan to transfer to Chico State is under 25% at c=99%.