# Question

A machine that packages 500-gram boxes of sugar-coated wheat cereal is being studied. The weights for a random sample of 100 boxes of cereal packaged by this machine are given in the attached file.

The quality control analyst wants to estimate the actual amount of sugar-coated wheat cereal contained in 500-gram boxes produced. It is known from the manufacturing specifications that the standard deviation of the amount of wheat cereal is equal to 9.4 grams.

1. Set up a 99% confidence interval estimate of the population mean wheat cereal weight.

2. On the basis of your results, do you think that the quality control analyst has a right to complain to the production manager? Why?

3. Does the population amount of sugar-coated wheat cereal per box have to be normally distributed here? Explain.

4. Explain why an observed value of 509.4grams for an individual box is not unusual, even though it is outside the confidence interval you calculated.

5. Suppose that you used a 95% confidence interval estimate. What would be your answers to 1.1 and 1.2?

The quality control analyst wants to estimate the actual amount of sugar-coated wheat cereal contained in 500-gram boxes produced. It is known from the manufacturing specifications that the standard deviation of the amount of wheat cereal is equal to 9.4 grams.

1. Set up a 99% confidence interval estimate of the population mean wheat cereal weight.

2. On the basis of your results, do you think that the quality control analyst has a right to complain to the production manager? Why?

3. Does the population amount of sugar-coated wheat cereal per box have to be normally distributed here? Explain.

4. Explain why an observed value of 509.4grams for an individual box is not unusual, even though it is outside the confidence interval you calculated.

5. Suppose that you used a 95% confidence interval estimate. What would be your answers to 1.1 and 1.2?

## Answer to relevant Questions

John Halikias, plant manager at HOU Vacuum Products, located in Patras, Ahaia, applies statistical thinking in his workplace. As a major supplier to automobile manufacturers, HOU wants to be sure that the leak rate (in cubic ...We plan to operate a professional dishwasher. We need to choose between two types of tablets: Kalgonit and Ludwig. One jumbo-pack of the former costs $200 and lasts for 3 years. The latter are two times cheaper but last for ...An airline plans to initiate service at an airport in a city of approximately 500,000 people. To determine staffing requirements, officials for the airline take advantage of the sample survey data on the relationship between ...a) Calculate the probability of a type ii error for the following hypotheses when µ = 37: ho: µ = 40 h1: µ < 40 The significance level is 5%, the population standard deviation is 5, and the sample size is 25. b) ...Researchers wanted to explore self-esteem in adolescent boys and adolescent girls. They used a 5-point Likert-type self-esteem inventory; a 1 = strongly disagree and 5 = strongly agree. Their results yielded the following t ...Post your question

0