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ygrant03
26.09.2019 •
Mathematics
Calculate the upper and lower limit for a 95% confidence interval about this mean.
a family needs a new car, but isn't sure they can fit the payment into their budget. a sample of 36 months of grocery bills yields a mean of $94 with a standard deviation of $10. if the upper limit of a 95% confidence level is below $100, the family can afford to buy the car.
standard error = (standard deviation)/(square root of sample size)
upper limit (dollars and cents)
lower limit (dollars and cents)
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Ответ:
We also have the number of samples, n = 36 and the confidence level, α = 95%
The formula for confidence interval is given
μ + z* (σ/√n) and μ - z* (σ/√n)
Where z* is the z-values for the confidence level
z* for 95% level of confidence is 1.96
Substitute this into the formula, we have
Upper limit ⇒ 94+(1.96)(10÷√36) = 94+(1.96)(10/6) = $97.27
Lower limit ⇒ 94 - (1.96)(10÷√36) = 94 - (1.96)(10/6) = $90.73
Ответ: