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I have TI 84

A sample of18small bags of the same brand of candies was selected. Assume that the population distribution of bag weights is normal. The weight of each bag was then recorded. The mean weight was3ounces with a standard deviation of0.13ounces. The population standard deviation is known to be 0.1 ounce.

NOTE: If you are using a Student'st-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

• Part (a)
• Find the following. (Round your answers to two decimal places.)
• (i)x=
• (ii)=
• (iii)s_x=
• Part (b)
• In words, define the random variableX.
• the number of candies in a bag
• the weight, in ounces, of a piece of candy
• the weight, in ounces, of one bag of candy
• the mean weight of the candies
• Correct! The variable of interest is the weight of one bag of candy.
• Part (c)
• In words, define the random variableX.
• the mean weight, in ounces, for the sample of 18 bags
• the mean number of candies for the sample of 18 bags
• the mean number of candies from each bag that weigh 3 ounces
• the mean weight, in ounces, of the pieces of candy
• Correct!Xrepresents the mean weight of all 18 bags of candy.
• Part (d)
• Which distribution should you use for this problem? (Round your answers to three decimal places.)
• X~
• ?
• B
• U
• Exp
• N
• H
• ,
• Explain your choice.
• The standard normal distribution should be used because the population standard deviation is known.
• The standard normal distribution should be used because the sample standard deviation is known.
• The Student'st-distribution should be used because the sample standard deviation is given.
• The Student'st-distribution should be used because the sample size is small.
• Incorrect. Although the sample standard deviation is given, the population standard deviation is known, so this distribution should not be used.
• Part (e)
• Construct a 90% confidence interval for the population mean weight of the candies.
• (i) State the confidence interval. (Round your answers to three decimal places.)
• ,
• (ii) Sketch the graph.
• (iii) Calculate the error bound. (Round your answer to three decimal places.)
• Part (f)
• Construct a 98% confidence interval for the population mean weight of the candies.
• (i) State the confidence interval. (Round your answers to three decimal places.)
• ,
• (ii) Sketch the graph.
• (iii) Calculate the error bound. (Round your answer to three decimal places.)
• Part (g)
• In complete sentences, explain why the confidence interval in part (f) is larger than the confidence interval in part (e).
• The confidence interval in part (f) is larger than the confidence interval in part (e) because the population standard deviation changes for each sample.
• The confidence interval in part (f) is larger than the confidence interval in part (e) because the mean weight changes for each sample.
• The confidence interval in part (f) is larger than the confidence interval in part (e) because a small sample size is being used.
• The confidence interval in part (f) is larger than the confidence interval in part (e) because a larger level of confidence increases the error bound, making the interval larger.
• Incorrect. The sample size is the same for both intervals; therefore, the size of the sample does not have any effect on the size of the confidence interval.
• Part (h)
• In complete sentences, give an interpretation of what the interval in part (f) means.
• There is a 98% chance that a small bag of candies weighs between these values.
• We are 98% confident that a small bag of candies weighs between these values.
• We are 98% confident that the true population mean weight of all small bags of candies is between these values.
• We are 98% confident that the mean weight of the sample of 18 small bags of candies is between these values.
• Incorrect. A confidence interval is based on a claim about a population parameter and not a sample.

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ILLOWSKYINTROSTAT1 8.HW.100.

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What is meant by the term "90% confident" when constructing a confidence interval for a mean?

If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the true value of the population mean.

If we took repeated samples, the sample mean would equal the population mean in approximately 90% of the samples.

If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the sample mean.

If we took repeated samples, approximately 90% of the samples would produce the same confidence interval.

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