30. The data represents a sample of the number of home fires started by candles

Question

30. The data represents a sample of the number of home fires started by candles for the past 7 ycars in a certain city 5460 5900 6090 6310 7160 8480 9930 (Check yourself. the sample mean is 7047 and sample standard deviation is 1616) a. Identify the variable in this set up b. Identify an individual in this set up c. Find and interpret the 99% confidence interval for the mean number of hone fires started by candles each year, assume normal distribution. Does the confidence interval, at 99% confidence level, provide sufficient evidence that the mean number of home fires started by candles in this city is greater than 5000 per year d. Write an appropriate inequality to justify your answer.

Explanation / Answer

Part a

The variable in this set up is given as the number of home fires started by candles.

Part b

An individual in this set up is the single home fire started by candles.

Part c

Here, we have to find 99% confidence interval for mean number of home fires started by candles.

Confidence interval = Xbar -/+ t/2, n – 1*S/sqrt(n)

From given data, we have

Sample mean = Xbar = 7047.142857

Sample standard deviation = S = 1616.124111

Sample size = n = 7

Degrees of freedom = df = n – 1 = 7 – 1 = 6

Confidence level = 99% (c = 0.99, = 0.01)

Critical value = t/2, n – 1 = 3.7074 (by using t-table or excel)

Confidence interval = 7047.142857 -/+ 3.7074*1616.124111/sqrt(7)

Confidence interval = 7047.142857 -/+ 3.7074* 610.837498

Confidence interval = 7047.142857 -/+ 2264.6361

Lower limit = 7047.142857 - 2264.6361 = 4782.507

Upper limit = 7047.142857 + 2264.6361= 9311.779

Confidence interval = (4782.51, 9311.78)

Part d

Here, we have to test H0: µ = 5000 versus Ha: µ > 5000

The value lies within confidence interval (4782.51, 9311.78), so we do not reject the null hypothesis that mean number of home fires started by candles in this city is 5000.

There is insufficient evidence to conclude that mean number of home fires started by candles in this city is greater than 5000. If value of µ is greater than upper limit of confidence interval, then there would be sufficient evidence to conclude that mean number of home fires started by candles in this city is greater than 5000.

The 99% confidence interval does not provide sufficient evidence to conclude that mean number of home fires started by candles in this city is greater than 5000.

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