Statistics Questions

Question

1. You measure 23 watermelons' weights, and find they have a mean weight of 64 ounces. Assume the population standard deviation is 13.2 ounces. Based on this, construct a 90% confidence interval for the true population mean watermelon weight. Give your answers as decimals, to two places
2. _____ ± _____ ounces
3. Assume that a sample is used to estimate a population proportion p. Find the 90% confidence interval for a sample of size 281 with 67 successes. Enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places.
4. 90% C.I.= ______

Answer 1

Confidence Interval for population mean:

sample mean +/- z-critical value*standard error

standard error = standard deviation/square root of sample size

sample mean = 64

standard deviation = 13.2

sample size = 23

z-critical value is z-score from standard normal probability table associated with 0.95 probability

Confidence interval for population proportion

sample proportion +/- z-critical value*standard error

sample proportion = number successes/sample size

standard error = square root (sample proportion * (1 - sample proportion)/sample size)

sample size = 281

number of successes = 67

z-critical value is z-score from standard normal probability table associated with 0.9 probability