Question

A federal agency responsible for enforcing laws governing weights and measures routinely inspects packages to determine whether the weight of the contents is as advertised on the package. The agency will only take action if there is strong evidence that the packages are underfilled. A random sample of 14 containers was taken and the contents weighed, with the weights given below. The containers are labeled to have 9 ounces. In your role as a member of this crack federal team, you are to specify and carry out an appropriate hypothesis test to determine whether there is enough evidence to support this claim. (Use a 10% significance level.) 8.778.738.598.58.538.988.59.058.699.089.129.079.148.99 8.77 8.59 8.53 8.5 8.69 9.12 9.14 8.73 8.5 8.98 9.05 9.08 9.07 8.99 A. The value of the standardized test statistic:

Answer 1

H0: Null Hypothesis: 9

HA: Alternative Hypothesis: <9

From the given data the following statistics are calculated:

n = 14

= 123.74/14 = 8.8386

s = 0.2472

SE = s/

= 0.2472/

= 0.0661

Test statistic is given by:

t = (8.8386 - 9)/0.0661

= - 2.4418

So,

The value of the standardized test statistic :

- 2.4418

ndf = 14 - 1 = 13

= 0.10

From Table, critical value of t = - 1.3502

Since calculated value of t = - 2.4418 is less than critical value of t = - 1.3502, the difference is significant. Reject null Hypothesis.

Conclusion:
The data support the claim that the packages are underfilled.

Answer to question asked:

The value of the standardized test statistic :

- 2.4418