Question

The average weight and the variance of 10,000 cans of soup is 83 and 9 kg. The distribution of weights is unknown. What is the hypothesis statistic for testing Ho : µ = 80 vs. H1 : µ ≠ 80 ?

Answer 1

Let us first find out the distribution of weights to choose appropriate hypothesis test.

Since the given problem is to test whether the population mean is significantly different from 80 and the population standard deviation is unknown, we use "ONE SAMPLE T TEST" to test this claim.

Thus the distribution of weights follow student t distribution with degrees of freedom.

GIVEN:

Sample size of soup cans

Sample mean weight

Sample variance

Sample standard deviation

HYPOTHESIS:

The hypothesis is given by,

(That is, the population mean weight of soup cans is not significantly different from 80 kg.)

(That is, the population mean weight of soup cans is significantly different from 80 kg.)

LEVEL OF SIGNIFICANCE:

TEST STATISTIC:

which follows t distribution with degrees of freedom.

CRITICAL VALUE:

The two tailed t critical value with degrees of freedom at significance level is .

CALCULATION:

DECISION RULE:

CONCLUSION:

Since the calculated t test statistic (100) is greater than the critical value (1.96), we reject null hypothesis and conclude that the population mean weight of soup cans is significantly different from 80 kg.