Question

Let p denote the population proportion of years in which the daytime temperature in New York on Valentine's Day (February 14) is below the freezing point. It is known that in 98 out of the most recent 120 years, the daytime temperature in New York on February 14 was below the freezing point. Assume that this data represents a random sample from the population.

a) Construct a 99% confidence interval for p. Given the following R output:  

qt(0.01, df=119, lower=F) = 2.358,  qt(0.005, df=119, lower=F) = 2.618
qt(0.01, df=120, lower=F) = 2.357,  qt(0.005, df=120, lower=F) = 2.617
qnorm(0.01, lower=F) = 2.326,       qnorm(0.005, lower=F) = 2.575

b) Based on the confidence interval in part a, can you conclude that the true population proportion p is above 70%? Explain.

Answer 1

a)

Answer:

Explanation:

The confidence interval for the proportion is obtained using the formula,

Where,

(qnorm(0.005, lower=F) = 2.575)

b)

Answer:

Yes, we can conclude that the true population proportion p is above 70%

Explanation:

The proportion of 70% lies outside the 99% confidence interval limits and the lower limit of the 99% confidence = 72.6% which is greater than 70% hence there is sufficient evidence to conclude that the true population proportion p is above 70% at 99% confidence interval.