A researcher examined a random sample of 300 homes in a small city and found that 47 had solar panels installed on their roofs.
Use the sample to construct a 99% confidence interval for the proportion of all homes in the city that have solar panels installed on their roofs. What is the sample proportion? **Round to two decimal places
The population does not need to be normally distributed for the sampling distribution of to be approximately normally distributed. Because of the central limit theorem. The sampling distribution of is approximately normal.
Step-by-step explanation:
We have a random sample of size from a population with and . Because n is large enough (i.e., n > 30) and and are both finite, we can apply the central limit theorem that tell us that the sampling distribution of is approximatelly normally distributed, this independently of the distribution of the random sample. is asymptotically normally distributed is another way to state this.