Problem 2 (40 points total) Atlanta temperatures. According to weather.com HYPER
ID: 3313620 • Letter: P
Question
Problem 2 (40 points total) Atlanta temperatures. According to weather.com
HYPERLINK "https://weather.com/weather/tenday/l/USGA0028:1:US"https://weather.com/weather/tenday/l/USGA0028:1:US
the maximum temperatures in the next 10 days will be:
63, 69, 67, 68, 64, 65, 65, 67, 64, 54
a. (20 points) Construct a 95% confidence interval for the maximum daily temperatures at the beginning of December in Atlanta.
b. (10 points) Suppose you want to reduce the width of the 95% confidence interval to half the size obtained in part a. How many more data points are required in the sample in order to obtain the desired confidence interval width? Is this possible?
c. (10 points) According to historical data HYPERLINK "https://en.wikipedia.org/wiki/Atlanta#Climate"https://en.wikipedia.org/wiki/Atlanta#Climate, the mean maximum temperature in December in Atlanta is 70.8 F. Based on the current data, are we experiencing a cold spell, that is, is the temperature on the next 10 days significantly lower than the historical average? Draw the appropriate conclusions.
Explanation / Answer
a)
b)
95% CI width = 2ME = 4.9335
Required width = 4.9335/2 = 2.46675
i.e. ME = 2.46675/2 = 1.2334
Hence 30 more data points are required
CI for 95% n 10 mean 64.6 z-value of 95% CI 1.9600 std. dev. 3.979949748 SE = std.dev./sqrt(n) 1.25857 ME = z*SE 2.46675 Lower Limit = Mean - ME 62.13325 Upper Limit = Mean + ME 67.06675 95% CI (62.1332 , 67.0668 )Related Questions
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