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The desired weight is supposed to be 16 ounces, but the water-filling machine occasionally deviates from that amount and needs to be adjusted. Jack and Jill take a random sample of bottles from today's production and weigh the water in each. The weights (in ounces) are:

15.56, 15.56, 15.08, 16.4, 16.64, 16.57, 16.15, 15.64, 15.72, 15.78

You will use a hypothesis test to determine if the mean amount of water differs from what is desired and if the machine needs adjusting.

Fill in the blank with the test value.

\[ H_0: \mu = \ \_\_\_\_\_\_\_ \]

Answer :

Final answer:

In hypothesis testing, the question is whether the mean weight of the water in ounces is equal to the target weight of 16 ounces. This is expressed as a null hypothesis: H0 : μ = 16. The hypothesis test will determine if the observed difference is statistically significant, implying that the machine may need adjusting.

Explanation:

In this situation, you will utilize the hypothesis testing for means or averages. So, the null hypothesis will take the form H0 : μ = 16, where μ is the mean. Here, 16 is the standard or targeted value of the quantity you're measuring - the weight of the water in ounces.

The hypothesis test will determine whether the observed difference between the sample mean (average of the given data points) and the hypothesized mean (16 ounces) is statistically significant or could have happened by chance. If it is highly unlikely to have occurred by chance, the null hypothesis is rejected and it can be stated that the average weight of the water in ounces is different from 16, implying that the machine needs adjustments.

Measurement Results, Hypothesis Testing, and Variation in Data are essential concepts in statistical analysis that provide insights into how data deviates from expected patterns and how those deviations are addressed.

Learn more about Hypothesis Testing here:

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