Answer
a) Margin of Error = 0.684
Lower limit = 13.62
Upper limit = 14.98
b) If the population is not normally distributed, the conditions that need to be satisfied include
- large enough sample size n.
- population standard deviation must be known or provided.
- simple random sample must be used.
c) Yes, the result in (a) is valid as it satisfies every required condition required to calculate the confidence interval.
Step-by-step explanation
a) Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Sample mean = 14.3
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
Critical value at 93% confidence interval for sample size is obtained from the z-tables because the population standard deviation is known (2).
Critical value = 1.81
Standard error of the mean = σₓ = (σ/√n)
σ = standard deviation of the sample = 2
n = sample size = 28
σₓ = (2/√28) = 0.378
Confidence Interval = (Sample mean) ± (Margin of error)
93% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error)]
CI = 14.3 ± (1.81 × 0.378)
CI = 14.3 ± 0.684
93% CI = (13.62, 14.98)
b) If the population is not normally distributed, the conditions that need to be satisfied include
- large enough sample size n.
- population standard deviation must be known or provided.
- simple random sample must be used.
c) Yes, the result in (a) is valid as it satisfies every required condition required to calculate the confidence interval.
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