sample means
Suppose a particular company's crop of apples is approximately normally distributed with a mean of 15.5 grams and a standard deviation of 1.2 grams. If a SRS of 4 apples is selected, what is the mean and the standard deviation of the sampling distribution of the sample means?
mean - 15.5 grams
standard deviation - 0.6
p - the true proportion
For a random sample from a skewed population, for which of the following sample sizes would the sampling distribution of the sample mean be closest to normal in shape: 4, 10, 40, 60?
60
According to the US Census, 23.5% of people in the US are under the age of 18. In a random sample of 250 residents of a small town in Ohio, 28% of the sample was under 18. What variable is equal to 23.5%
population proportion
The distribution of actual weights of 8 ounce chocolate bars is normal with mean 8.1 ounces and standard deviation of 0.1 ounces. Find the probability that the mean weight of 40 randomly selected candy bars is less than 8 ounces.
0
There are 100 seniors at St. Paul's. Mrs. Gill conducts a poll that asks 20 randomly selected seniors how many hours of sleep they got last night. She finds that the mean amount of sleep is 6.7 hours. The population standard deviation is 2 hours. Estimate the standard deviation of the sampling distribution of the sample means.
We can't because the 10% condition does not hold.
For which of the following will the sample proportion tend to differ least from sample to sample:
a. random samples of size 30 with p=0.1
b. random samples of size 40 with p=0.1
c. random samples of size 40 with p=0.4
d. random samples of size 50 with p=0.5
e. random samples of size 60 with p=0.5
E
A random sample is to be selected from a population. For which combination of n and p is it reasonable to assume that the sampling distribution of the sample proportion will be approximately normal:
a. n=10, p=0.4
b. n=25, p=0.5
c. n=30, p=0.2
d. n=40, p=0.1
e. n=100, p=0.05
B. n=25, p=0.5
According to the US Census, 23.5% of people in the US are under the age of 18. In a random sample of 250 residents of a small town in Ohio, 28% of the sample was under 18. What variable is equal to 28%?
It is estimated that 58% of all Americans sleep on their sides. In a random sample of 350 Americans, what is the probability that at least 50% sleep on their side?
0.9988
Population 1 is normally distributed with a mean of 40 and a standard deviation of 4, and population 2 is normally distributed with a mean of 25 and a standard deviation of 7. Suppose we select independent SRSs of n1=100 and n2=85 from population 1 and 2. Which of the following are the values of the mean and standard deviation of the sampling distribution of the difference in sample means?
15 mean
0.858 standard deviation
An electronic prize wheel is programmed to land on win 25% of the time on weekdays and 10% of the time on weekends, and consecutive plays produce winners independently. Suppose we observe a random sample of 50 outcomes from this machine on weekdays and 100 outcomes from this machine on weekends. Describe the shape, center, and spread of the sampling distribution of the difference in proportions (weekday-weekend).
shape - approximately normal
center - 0.15
standard deviation - 0.07
A sample of size n is to be selected from a population with population proportion p. For the sampling distribution of the sample proportion to be approximately normal, what condition needs to be checked?
np and n(1-p) are both greater than or = 10
According to the US Census, 23.5% of people in the US are under the age of 18. In a random sample of 250 residents of a small town in Ohio, 28% of the sample was under 18. What variable does 250 represent?
sample size
Suppose a particular company's crop of apples is approximately normally distributed with a mean of 15.5 grams and a standard deviation of 1.2 grams. If a SRS of 4 apples is selected, what is the probability that the mean weight of the sample is less than 14 grams?
0.9938