Answer:
a. =50 ± 4.67
b. =50 ± 4.81
decreasing the sample size increase the margin of error
c. =50 ± 3.51
decreasing the confidence level reduced the margin of error
d. No. because the confidence interval coefficient is gotten from the table of normal distribution of Z value. therefore the confidence interval is only used for normal distributed population
Step-by-step explanation:
given
The sample mean, x, = 50,
the sample standard deviation, s, = 8.
a. Construct a 98% confidence interval for m if the sample size, n, is 20
for a 98% confidence interval of an infinite population, thus for a sample of size N and mean x, drawn from an infinite population having a standard deviation of σ, the mean value of the population is estimated to by:
x±
2.33σ /√N
for a confidence level of 98%, Zc = 2.33 gotten from the table of confidence interval.
This indicates that the mean value of the population lies between
50- (
2.33*8 /√20) and 50+ (
2.33*8 /√20)
with 98% confidence in this prediction.
=50 ± 4.67
=45.33 or 54.67
(b) Construct a 98% confidence interval for m if the sample size, n, is 15.
using the same method as above
x±
2.33σ /√N
This indicates that the mean value of the population lies between
50- (
2.33*8 /√15) and 50+ (
2.33*8 /√15)
=50 ± 4.81
=45.19 or 54.81
decreasing the sample size increase the margin of error
(c) Construct a 95% confidence interval for m if the sample size, n, is 20. Compare the results to those obtained in part
95% confidence interval =1.96 (gotten from table of confidence coefficient)
using x±1.96
σ /√N
This indicates that the mean value of the population lies between
50- (1.96
*8 /√20) and 50+ (1.96
*8 /√20)
=50 ± 3.51
=46.49 or 53.51
c. decreasing the confidence level reduced the margin of error
(d) Could we have computed the confidence intervals in parts (a)–(c) if the population had not been normally distributed?
No. because the confidence interval coefficient is gotten from the table of normal distribution of Z value. therefore the confidence interval is only used for normal distributed population
.