Management at a seaside resort is publishing a brochure and wants to include a statement about the proportion of clear days during their peak season. out of a random sample of 150 days from over the last two peak seasons, 117 days were recorded as clear. they want to estimate the proportion of clear days to within a 5% margin of error with a 95% confidence interval. what's the sample size necessary to construct this interval? a. 384b. 264c. 383d. 385e. 263

B. 264

Step-by-step explanation:

Formula to calculate the sample size 'n' , if the prior estimate of the population proportion (p) is available:

, where z = Critical z-value corresponds to the given confidence interval

E=  margin of error

Let p be the population proportion of clear days.

As per given , we have

Prior sample size : n= 150

Number of clear days in that sample = 117

Prior estimate of the population proportion of clear days =

E= 0.05

The critical z-value corresponding to 95% confidence interval = z*= 1.95 (By z-table)

Then, the required sample size will be :

Simplify ,

Hence, the sample size necessary to construct this interval =264

Thus the correct option is B. 264