An analyst from an energy research institute in California wishes to precisely estimate the 98% confidence interval for the average price of unleaded gasoline in the state. In particular, she does not want the sample mean to deviate from the population mean by more than B dollars given on the right. What is the minimum number of gas stations that she should include in her sample if she believes the standard deviation is approximately σ (shown on the right), as reported in the popular press?
| B = | 0.120 |
| σ = | 0.800 |
| a | 242 |
| b | 16 |
| c | 14 |
| d | 171 |
| e | None |
The following information is provided,
Significance Level, α = 0.02, Margin or Error, E = 0.12, σ =
0.8
The critical value for significance level, α = 0.02 is 2.33.
The following formula is used to compute the minimum sample size
required to estimate the population mean μ within the required
margin of error:
n >= (zc *σ/E)^2
n = (2.33 * 0.8/0.12)^2
n = 241.28
Therefore, the sample size needed to satisfy the condition n
>= 241.28 and it must be an integer number, we conclude that the
minimum required sample size is n = 242
Ans : Sample size, n = 242
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