Question

the life of a 60-watt light bulb in hours is known to be normally distributed with a 25 hours. create 5 different random samples of 100 bulbs each which has a mean life of x bar 1000 hours and perform one-way anova with state it. Please solve using Excel and explain it clearly

Answer 1

solution

The function

$$=NORMINV(RAND(), mean, standard\ deviation)$$

Is used to generate random numbers from a normal distribution with $Mean =1000$ and $Standard \ deviation=25$

The formula is drugged down to create 100 rows and right to create 5 columns. Each column representing one sample of size 100. The 5 samples are found to have the following distribution:

$$Sample \ 1: \ Mean = 996.92, \ Variance = 615.996$$ $$Sample \ 2: \ Mean = 994.29, \ Variance = 593.588$$ $$Sample \ 3: \ Mean = 997.471, \ Variance = 698.00$$ $$Sample \ 4: \ Mean = 994.46, \ Variance = 586.580$$ $$Sample \ 5: \ Mean = 1000.08, \ Variance = 572.223$$

One way ANOVA tests the null hypothesis that the samples are drawn from populations with equal means. The hypothesis is rejected if the P-value from the test is less than the required $\alpha$ level $(0.05)$ or if the F test statistic is greater than the critical value. The F test is useful when comparing 3 or more samples.

One way ANOVA for the 5 samples results in:

$P-value = 0.0038$

$F\ critical \ value = 2.3899$

$F-test\ statistic= 3.923$

answer: the samples are drawn from populations with different means