An airline researcher studied reservation records for a random sample of 100 day

Question

An airline researcher studied reservation records for a random sample of 100 days in order to estimate u,the mean number of persons who fail to keep their reservation (no shows) on the morning flight from islamabad to karachi.the summary of the data revealed the values of xbar=1.50 answer s^2 = 1.404
sometimes after this study,the airline instituted a new reservation system that discourages customers from holding simultaneous reservation on different flights to the same destination. it is now desired to estimate the mean number of no show for the morning flight.for this purpose a95% confidence interval with a width of 0.50is required
1_ how many days should be included in the sample to prepare this estimate
2_if the desired confidence coefficient was increased to 99% (other factor remaining the same) how many days would have to be included in the sample. comment on the difference between the two sample sizes
3_what is the likely effect on the confidence interval if the population variability is too large

Explanation / Answer

Part (1)

Sample size. n, required to estimate the population mean µ with 100(1 - )% confidence within an error margin of E is given by

n = (s2 t2n – 1,/2)/E2, where s2 = sample variance and tn – 1,/2 is the upper (/2) percent point of t-distribution with (n - 1) degrees of freedom and n is the size of sample on which s2 was calculated. .

So, given s2 = 1.404 based on a sample of size 100, E = 0.5 and from Statistical Tables, t99, 0.025 = 1.984,

sample size. n, required to estimate the population mean µ with 90% confidence within an error margin of 0.5 is: (1.404 x 1.9842)/0.52 = 31.04 ~ 32

So, 32 days should be included in the sample to prepare this estimate. ANSWER

Part (2)

If the desired confidence coefficient was increased to 99% (other factor remaining the same) 54.37 or 55 days would have to be included in the sample. [just replace 1.984 by 2.626 in the working of Part (1)]

As we increase the confidence level, the sample size also would increase.
ANSWER

Part (c)

Effect on the confidence interval if the population variability is too large is that the interval would get wider.

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