Based on a random sample of 25 units of product x, the average weight is 102 lb and the sample standard deviation is 10 lb. we would like to decide if there is enough evidence to establish that the average weight for the population of product x is greater than 100 lb. therefore, the alternative hypothesis can be written as ha: μ > 100. (assume the population is normally distributed.)

Question

Gabrielle

Mathematics

22 October, 17:37

Based on a random sample of 25 units of product x, the average weight is 102 lb and the sample standard deviation is 10 lb. we would like to decide if there is enough evidence to establish that the average weight for the population of product x is greater than 100 lb. therefore, the alternative hypothesis can be written as ha: μ > 100. (assume the population is normally distributed.)

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Answers (1)

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Corinne Walters · Answer 1

Missing part of the question: Use level of significance of 0.035.

Solution:

Null hypothesis: u = 100

Alternative hypothesis: u >100

The next step is to calculate Z value for X = 100.

That is,

Z = [ (mean - X) (Sqrt (n)) ]/SD = (102-100) [Sqrt (25) ]/10 = 10/10 = 1

From Z table

P (X=100) = P (Z) = P (1) = 0.8413

Then,

P (X>100) = 1 - P (X=100) = 1-0.8413 = 0.1587

Since

P (X>100) > Significance level considered (0.035), null hypothesis is rejected. That is, the evidence is not significant to suggest that weight of the population is greater than 100 lb.