Question

A soil distributor sells fertilizer in 10 kg bags. A customer feels that the distributor sells underweight bags. To support his hunch, he purchases 8 bags of soil. They have an average weight of 9.75 kg with standard deviation 0.7 kg. Does the customer have a case against the distributor? Test using α = 0.05.

Answer 1

Solution :

1) The null and alternative hypotheses would be as follows:

kg

kg

Test statisic :

To test the hypothesis the most appropriate test would be one sample t-test. The test statistic is given as follows:

Where, x̅ is sample mean, μ​​​​​ is hypothesized value of population mean under H​​​​​​​​​​​​0, s is sample standard deviation and n is sample size.

We have,  x̅ = 9.75 kg,  μ = 10 kg, s = 0.7 kg, n = 8

The value of the test statistic is -1.0102.

P - value :

Since, our test is left-tailed test, therefore we shall obtain left-tailed p-value for the test statistic. The left-tailed p-value is given as follows :

p-value = P(T < t)

p-value = P(T < -1.0102)

p-value = 0.1730

The p-value is 0.1730.

Significance level (α) = 0.05

(0.1730 > 0.05)

Since, p-value is greater than the significance level of 0.05, therefore we shall be fail to reject the null hypothesis (H​​​​​​0) at 0.05 significance level.

Conclusion : At 0.05 significance level, there is not sufficient evidence to conclude that the distributor sells underweight bags.

Hence, customer does not have a case against the distributor.

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