A new solar collector is being tested for use in charging batteries that can provide electricity for an entire home. A random sample of days was selected and the amount of solar radiation was measured...

A new solar collector is being tested for use in charging batteries that can provide electricity for an entire home. A random sample of days was selected and the amount of solar radiation was measured (x, in langleys) for each. The total battery charge was measured as a proportion (y, between 0 and 1). The summary statistics are given below

a. What proportion of a charge can you expect the batteries to take if the amount of solar radiation is 100 langleys?

b. Find a 95% confidence interval for the true mean battery charge proportion if the amount of solar radiation is 130 langleys.

c. A value of 80 langleys indicates a typical cloudy day. On a typical cloudy day, is there any evidence to suggest that the true mean charge proportion is greater than 0.06 (the proportion needed to ensure a home will have sufficient energy until the next day)? Use a significance level of 0.01.