Answer :
Using a 98% confidence interval, the total number of customers that should be sampled is 87.
What exactly is sample size?
The sample size refers to the number of observations in the data set, and as the sample size increases, the calculated value of population parameters becomes more reliable and true. In other words, as sample size increases, the value of the margin of error decreases.
Given,
Standard deviation σ=300
Confidence level: 0.98
Maximum allowable error: ε=75
The critical value is calculated using the standard normal table at the level of significance (0.02)
The critical value in this case is 2.326.
Sample size is calculated by,
n=((Z[tex]z_{\alpha /2}[/tex])²×σ²))/ε²
n=((2.326)²×(300)²)/(75)²
n=86.564≈87
Therefore, the required sample size is 87.
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