Question

The inspection division of the Lee County Weights and Measures Department is interested in estimating the...

The inspection division of the Lee County Weights and Measures Department is interested in estimating the actual amount of soft drink that is placed in 2-liter bottles at the local bottling plant of a large nationally known soft-drink company. The bottling plant has informed the inspection division that the standard deviation for 2-liter bottles is 0.05 liter, i.e. the population standard deviation is σ = 0.05. A random sample of one hundred 2-liter bottles obtained from this bottling plant indicates a sample average of 1.99 liters.

1. [5 points] Set up a 95% confidence interval estimate of the true average amount of soft drink in each bottle. What is the margin of error?

2. [4 points] Based on your answer to part 1, can we reject the null hypothesis H0 : µ = 2 vs. HA : µ ≠ 2 at a 95% confidence level? Explain.

3. [5 points] What would be your answer to previous question if n = 121? What about if n = 81? What is the range of the sample size such that the above hypothesis is rejected?

4. [8 points] Suppose now that Lee County requires these measurements in ounces instead (1 liter=33.8 ounces). Call this variable Y , that is Y = 33.8X. (a) [2 points] What is the mean of the sample in ounces? (Recall x¯ = 1.99) (b) [2 points] Whatisthe standard deviation ofthe population in ounces? I.e. whatisσy?(Recall σx =0.05) (c) [4 points] What is the margin of error for a 95% confidence interval for the amount of soft drink in a bottle in ounces? Compare your answer to the one in part 1. Hint: Compare the ratio of the margin of errors, using the one for ounces in the numerator. ∗

5. [8points]Let's go back to liters.Assume that we no longer haveσ but we calculateds=0.048 fromthe sample. (a) [3 points] Construct the test statistic for the hypothesis H0 : µ = 2 vs. HA : µ ≠ 2. (b) [5points] Whatisthe(approximate) criticalt value that we should compare this statistic to if we want to use a 90% confidence? For 95% confidence? For 99% confidence? Do you reject the null hypothesis at any ofthese levels?What educated guess can youmake aboutthe p-value of this test?

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
If the inspection division of a county weights and measures department wants to estimate the mean...
If the inspection division of a county weights and measures department wants to estimate the mean amount of? soft-drink fill in? 2-liter bottles to within plus or minus0.02 liter with 95?% confidence and also assumes that the standard deviation is 0.09 ?liters, what sample size is? needed?
We are interested in estimating the mean amount of rain last month in our county. It...
We are interested in estimating the mean amount of rain last month in our county. It is known that the population standard deviation is 1.5 inches generally for the month of interest. 49 instruments that measure rainfall were placed throughout the county randomly. The sample mean from the instruments was 5.2 inches. Calculate a 95% confidence interval for the population mean of rainfall last month in the county. [Reference: Table A: Standard Normal Probabilities] 4.78 to 5.62 4.85 to 5.55...
3. We are interested in estimating the mean annual income of adults in Sweetwater County. To...
3. We are interested in estimating the mean annual income of adults in Sweetwater County. To accomplish this, we select a random sample of 65 adults residing in the county. We find that the sample mean is $47,250, and we know from the previous studies that the population standard deviation is $3,555. a) Calculate a 95% confidence interval for the population mean, and interpret the result. B) Calculate a 99% confidence interval for the population mean, and interpret the result....
The Crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles...
The Crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles of the popular Crown Classic Cola soft drink. Both overfilling and underfilling bottles are undesirable: Underfilling leads to customer complaints and overfilling costs the company considerable money. In order to verify that the filler is set up correctly, the company wishes to see whether the mean bottle fill, μ, is close to the target fill of 16 ounces. To this end, a random sample...
The Crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles...
The Crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles of the popular Crown Classic Cola soft drink. Both overfilling and underfilling bottles are undesirable: Underfilling leads to customer complaints and overfilling costs the company considerable money. In order to verify that the filler is set up correctly, the company wishes to see whether the mean bottle fill, μ, is close to the target fill of 16 ounces. To this end, a random sample...
4. Two machines are used for filling glass bottles with a soft-drink beverage. The filling processes...
4. Two machines are used for filling glass bottles with a soft-drink beverage. The filling processes have known standard deviations s1 = 0.010 L, and s2 = 0.015 L, respectively. A random sample of n1 = 25 bottles from machine 1 and n2 = 20 bottles from machine 2, results in average net contents of ?̅ # = 2.04 L, and ?̅ $ = 2.07 L. a. Test the hypothesis that both machines fill to the same net contents, using...
A random sample of n = 500 books is selected from a library and the number...
A random sample of n = 500 books is selected from a library and the number of words in the title of each book is recorded. The sample mean number of words in the title is 6.2 words. The population variance is 40 words^2 . Please show how to do each one using R and Rstudio. a) (2 points) Compute the z-statistic for testing the null hypothesis H0 : µ = 7. b) (3 points) Perform a level ? =...
To compare prices of two local stores, a random sample of items that are sold in...
To compare prices of two local stores, a random sample of items that are sold in both stores were selected and their price noted in the first weekend of the year: (12 marks) Item Store A Store B Difference (Store A - Store B) 1 1.65 1.99 -0.34 2 8.70 8.49 0.21 3 0.75 0.90 -0.15 4 1.05 0.99 0.06 5 11.30 11.99 -0.69 6 7.70 7.99 -0.29 What are the null and alternative hypothesis if we want to confirm...
Do all the following problems. I. Choose the best answer for each multiple choice. Please use...
Do all the following problems. I. Choose the best answer for each multiple choice. Please use CAPITAL letters to indicate your answer and write neatly. (30 points) 1. ____ 4.____ 7. ____ 10.____ 13. ____ 2. ____ 5.____ 8. ____ 11.____ 14. ____ 3. ____ 6.____ 9. ____ 12.____ 15. ____ Whenever the population standard deviation is unknown and the population has a normal or near-normal distribution, which distribution is used in developing an interval estimation? A. standard distribution B....
To compare prices of two grocery stores in Toronto, a random sample of items that are...
To compare prices of two grocery stores in Toronto, a random sample of items that are sold in both stores were selected and their price noted in the first weekend of July 2018: (12 Points) Item Store A Store B Difference (Store A - Store B) 1 1.65 1.98 -0.33 2 8.70 8.49 0.21 3 0.75 0.89 -0.14 4 1.05 0.99 0.06 5 11.30 11.99 -0.69 6 7.70 7.99 -0.29 7 6.55 6.99 -0.44 8 3.70 3.59 0.11 9 8.60...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT