Formulas
point estimate & margin of error for mean (Population St. Dev. Known)
Point Estimate: hatx = (sumx)/n
Margin of Error: E = Z_c *sigma/sqrtn
Find the point estimate based off of the following information:
99% Confidence level, n= 827, x=174
Round to 4 decimal places
0.2104
A continuous uniform distribution has outcomes between 1 to 19, find
P(6<x<12)
6/18 = 1/3 or .3333...
In a telephone poll of 1012 adult Americans, 11% of the respondents said that Regan was a great president. Give a 98% confidence interval for the proportion of all adult Americans who think Regan was great.
(0.087, 0.133)
A laboratory tested 83 smoothies from the mega menu at Smoothie Uniiverse and found that the sample mean number of calories was 233 and sx=12.9 ounces. Construct a 95% confidence interval for the true mean of calories of all such smoothies.
(230.183, 235.817)
point estimate & margin of error for proportions
Point Estimate: hatp =x/n
Margin of Error:
E = Z_c *sqrt((hatp hatq)/n)
Find the point estimate of the proportion of people who enjoy reading, in a random sample of 749 people, 61 enjoyed reading.
“p-hat”=0.08
A normal distribution has a mean of 64 and a standard deviation of 3.2, find and round to 4 decimal places.
P(x<60)
10.56% or .1056
Of 367 randomly selected students, 30 said that they planned to work in a rural community. Find a 95% confidence interval for true proportion.
(0.054, 0.110)
Suppose you want to construct a 95% confidence interval for the average speed that cars travel on the highway. You want a margin of error of no more than plus or minus 0.5 mph and know that the population standard deviation is 7 mph. At least how many cars must you clock?
n=753
Given the confidence interval, the formula for
hatp and E
hatp = (upper + lower)/2
E = (upper -lower)/2
A confidence interval was constructed to estimate the proportion of smokers in the U.S. Use the confidence interval 0.167 < p < 0.458 to find the margin of error, E. Round answer to 3 decimal places.
E=0.146
The heights of a group of seven-year-old children are normally distributed with mean 117 cm and standard deviation 5 cm. A child is chosen at random from the group.
The probability that this child is shorter than k cm is 0.65. Find the value of k.
What is 119?
Suppose you want to construct a 90% confidence interval for the proportion of people who will stop to pick up a nickel if they see one on the ground. You want a margin of error of no more than plus or minus 4 percentage points. How many people must you survey?
n=423
Construct a 92% confidence interval of an experiment that found the mean temperature for the city in August was 101.82, with a population standard deviation of 1.2. There were 6 samples in this experiment.
100.96 < μ < 102.68