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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
Sxx = 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.
What is the parameter of interest in this situation? Give notation and define it.- What is the sample statistic in this situation? Give notation and define it.
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The point estimate for the difference between the proportions is:
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