7.3g Understand effect of sample size for Proportion

The percentage of people who prefer dogs to cats is 78% for a given population. What is the standard error of the sampling distribution of sample proportions for samples of size n=35, n=100, and n=250? Round all answers to the nearest hundredths if applicable.

If n=35, then σp̂= .07 If n=100, then σp̂= .04 If n=250, then σp̂= .03 use formula: σp̂ =√p(1−p)/n

A study shows that 64% of a population prefer to use the elliptical at the gym, compared to all other types of cardio equipment. What sample size would be needed to find a sample proportion such that the standard error of the sampling distribution is within 0.03 units of the population?

This means that in order to find the sample proportion for the sampling distribution with a given standard deviation of 0.03 a sample size of 256 would be needed. use formula: σp̂ =√p(1−p)/n

The proportion of people who make New Years Resolutions and keep them per year is 0.32. For what sample size, n, will the sampling distribution of sample proportions have a standard deviation of 0.10?

n=22 use formula: σp̂ =√p(1−p)/n standard deviation of sampling (σp̂ )=0.10 proportion p =0.32

Of last year, the percentage of investors that follow the buy low, sell high strategy was 56%. A financial analyst is conducting research on various investing strategies and plans to sample investors from their company. For what sample size, n, will the sampling distribution of sample proportions have a standard deviation of 0.03?

n=274 use formula: σp̂ =√p(1−p)/n

A doctor is concerned that hospital patients with minor injuries have longer than necessary hospital stays due to low nurse staffing. Of the last 5 years, the percentage of patients who had minor injuries and stayed at the hospital for over 3 days was 22%. If the doctor chooses to study this further, for what sample size n will the sampling distribution of sample proportions have a standard deviation of 0.15?

n=8 use formula: σp̂ =√p(1−p)/n