Question

# I need to know the formulas or excel functions required to make the correct determinations. As well as verify my

logic. Please use Excel where appropriate.

a. For the purposes of this question and the next only, suppose that the variable 'temp' is normally distributed with mean 20 and standard deviation 8. What is the probability that the temperature is between 8 and 31.3 degrees Celsius?

$P(19.84<X<20.16)=P(σx−μ <Z<σx−μ )=P(88−20 <Z<831.3−20 )=P(−1.5<Z<1.41)$

then

$P(−1.5<Z<1.41)=P(Z<1.41)−P(Z<−1.5)=0.9207−[1−P(Z<1.5)]=0.9207−[1−0.9332]=0.8539$

=NORM.DIST(31.3,20,8,TRUE)-NORM.DIST(8,20,8,TRUE)

b. Using the same information as in the question above, what is the probability that the average from a sample of size 128 is between 19.1 and 21?

$P(−1.27<Z<1.41)=P(Z<1.41)−P(Z<−1.27)=0.9207−[1−P(Z<1.27)]=0.9207−[1−0.898]=0.8187$

c. Use the data to estimate a 90% confidence interval on the (population) mean of temperature. Report the left side and the right side. Give the assumed probability that the confidence interval you just computed does not cover the true population mean of temperature.

Left Side 20.52 - 1.209767476

Right Side 20.52 + 1.209767476

Assumed probability that the confidence interval does not cover the True population mean jQuery22408795503103414575_1578083399588???

d. Suppose that in the past, the population proportion of days that were misty (weather of type 2) was 21%. Use a hypothesis test to determine if there is evidence in the data at the 5% level of significance to conclude that the proportion has changed. Write the null hypothesis and your alternative hypothesis. Define your p-value and hypothesis test conclusion.

Null hypothesis: The proportion is equal to 21%

Alternative hypothesis: The proportion is different from 21%

P-Value: 0.196292726

Hypothesis Conclusion: The P is lower than the null, so we will reject the null, There is enough evidence to conclude that the proportion has changed.

Data for the problem

temp 8.2 8.2 4.92 5.74 6.56 9.84 9.02 2.46 12.3 18.86 18.86 16.4 8.2 11.48 8.2 14.76 12.3 18.86 21.32 13.12 18.86 13.94 13.12 20.5 18.04 28.7 16.4 24.6 22.96 25.42 22.14 20.5 22.14 21.32 25.42 24.6 22.14 36.9 27.88 37.72 31.16 31.16 25.42 32.8 28.7 30.34 28.7 33.62 27.06 31.16 27.06 31.16 27.06 26.24 25.42 31.98 22.14 26.24 22.14 30.34 28.7 16.4 23.78 24.6 23.78 22.96 22.14 22.14 22.14 16.4 13.94 23.78 13.94 17.22 12.3 10.66 9.02 12.3 10.66 9.02 10.66 20.5 8.2 14.76 18.86 9.02 10.66 13.94 13.94 17.22 8.2 5.74 10.66 12.3 12.3 14.76 9.02 14.76 12.3 9.84 14.76 18.04 22.14 16.4 25.42 22.14 24.6 26.24 22.14 18.86 30.34 26.24 30.34 23.78 27.88 34.44 35.26 36.08 33.62 32.8 30.34 28.7 27.06 22.14 16.4 13.94 17.22 22.96

Alternative Hypothesis Data 21,21.........21

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