An experiment is conducted to compare two brands of kerosene heaters. The manufa

Question

An experiment is conducted to compare two brands of kerosene heaters. The manufacturer of brand A claims that his model will heat an 8-foot room from 60 degrees F to 70 degrees F in less time than a competitor’s brand B. Test the manufacturer’s claim if a random sample of 12 heaters is selected from brand B; an independent sample of 15 heaters is selected from brand A. The observations, shown below, are time in seconds to raise the room temperature as specified. Test (using Chapter 5 from Conover) at a = .05.

DATA:

Brand B                                          |   Brand A

______________________________________________________

    69.3     52.6     56.0     34.4 | 28.6     30.6     25.1     31.8

    22.1     60.2     47.6     43.8 | 26.4     41.6     34.9     21.1

    53.2     48.1     23.2     13.8 | 29.8     36.0     28.4     37.9

                                                              38.5     13.9     30.2

Explanation / Answer

Solution:

Here, we have to use two sample t test for the population mean.

H0: µ1 = µ2 versus Ha: µ1 < µ2

µ1 is the population mean for Brand A and µ2 is the population mean for Brand B.

The test statistic formula is given as below:

t = (X1bar – X2bar)/sqrt[(S1^2/N1)+(S2^2/N2)]

From the given data, we have

X1bar = 30.32

X2bar = 43.69167

S1 = 7.127833

S2 = 16.92295

N1 = 15

N2 = 12

= 0.05

Degrees of freedom = 15 + 12 – 2 = 25

Lower critical value = -1.7081

Test statistic = t = (30.32 - 43.69167)/sqrt[(7.127833^2/15)+( 16.92295^2/12)] = -2.7780

P-value = 0.0051

P-value < = 0.05

So, we reject the null hypothesis that both means are same.

There is sufficient evidence to conclude that the model A have average less time than model B.

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