Find a confidence interval for the true mean

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Reference no: EM131435941

Physical Sciences

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

β^{^}₀ = 0.2007

n = 21

MSE = 0.06135

β^{^}₁ = 0.00446

x‾ = 103.095

S_xx = 12335.8

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.

Reference no: EM131435941

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