Question

# 9. (19) A random sample of 64 UPW college students shows that the sample mean GPA...

9. (19) A random sample of 64 UPW college students shows that the sample mean GPA is 2.82 with a standard deviation of 0.45.

(a) Construct a 90% Confidence Interval for the mean GPA of all UPW students.

(b) If we want to be 95% confident, and we want to control the maximum error of estimation to 0.1, how many more students should be added into the given sample?

(c) Would you conclude that the mean GPA in UPW is lower than 3 at 5% level of significance?

a) For 90% Confidence interval, the critical value is z0.05 = 1.645

The 90% confidence interval is  = 2.82 +/- 0.09

= 2.73, 2.91

b) Margin of error = 0.1    c)  The test statistic is   P-value = P(Z < -3.2)

= 0.0007

Since the P-value is less than the significance level (0.0007 < 0.05), so we should reject the null hypothesis.

At 0.05 significance level, there is sufficient evidence to conclude that the mean GPA in UPW is lower than 3.

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