Variables: HS= heavy smoker; MS= moderate smoker; NS= non-smoker 1.Do the data p
ID: 3054307 • Letter: V
Question
Variables: HS= heavy smoker; MS= moderate smoker; NS= non-smoker
1.Do the data provide evidence that not all means are equal?
2.State the null and alternative hypotheses, specify the distribution of the test statistic under the null hypothesis, report the value of the test statistic, and the p-value of the test.
3. Conclusion about the length and the three variables
4.What is the pooled estimate of the variance?
Analysis of Variance results: Responses: LENGTH Factors: SMOKING Response statistics by factor SMOKING. nMean Std. Dev. Std. Error HS 48 3.6009523 0.60015871 19 49.3 2.5024433 0.57409985 NS 39 51.1 2.8974581 0.46396461 One sample T hypothesis test: Group by: SMOKING H: Mean of LENGTH Ho :=0 HA : = 0 36 MS ANOVA table Source DF SS M S F-Stat P-value SMOKING 2 181.37489 90.687447 9.3188167 0.0002 Error 91 885.58 9.7316484 Total 93 1066.9549 Hypothesis test results: SMOKING Sample Mean Std. Err. DF T-Stat P-value HS 48 0.60015871 35 79.978844Explanation / Answer
1. here the data provides enough evidence that the means are not equal to each other as p - value for the F test is less than the significance level 0.05.
2. Null hypothesis : H0: All population means are equal here. That means length for each of three categories of smokers is equal to each other.
Alternative Hypothesis : Ha : Atleast one piopulation mean differe from other population means. Here the distribution of test statistic is F distribution.
Value of Test statistic = 9.3188
p - value = 0.0002
so we reject the null hypothesis here.
3. Here we can conclude that there is enough evidence that the mean length is not equal for each catrgories of smokers. Similarly, all of the smoker categories has mean greater than 0.
4. Here pooled estimate of variance = SS(error) = 885.58
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