### Statistical Analysis of Pet Owners’ Shopping Preferences#### Question 1:From a sample of 250 pet owners, 104 indicate that they buy their pet food in brick-and-mortar stores.**a. Calculate the value of the sample statistic:**To find the sample statistic (proportion), use the formula:\[ \hat{p} = \frac{x}{n} \]Where:- \( \hat{p} \) is the sample proportion,- \( x \) is the number of successes (pet owners who buy pet food in brick-and-mortar stores),- \( n \) is the total sample size.Plugging in the numbers:\[ \hat{p} = \frac{104}{250} = 0.416 \]**b. Define the parameter this sample statistic estimates:**The parameter this sample statistic estimates is the proportion of all pet owners who buy their pet food in brick-and-mortar stores.**c. Calculate a 95% confidence interval for the parameter:**Given:- Sample proportion (\( \hat{p} \)) = 0.416- Standard error (\( SE \)) = 0.03117The formula for the confidence interval is:\[ \hat{p} \pm z \cdot SE \]For a 95% confidence interval, \( z \) (the critical value) is approximately 1.96.\[ CI = 0.416 \pm (1.96 \cdot 0.03117) \]Calculate the margin of error:\[ MOE = 1.96 \cdot 0.03117 = 0.0611 \]Thus, the 95% confidence interval is:\[ (0.416 - 0.0611, 0.416 + 0.0611) = (0.3549, 0.4771) \]**d. Interpret the 95% confidence interval in context:**We are 95% confident that the true proportion of all pet owners who buy their pet food in brick-and-mortar stores lies between 35.49% and 47.71%.**e. Meaning of 95% confidence interval:**Which of the following best explains the meaning of 95% confidence in this question? Check only one.- [ ] The proportion of 95% of all pet owners who buy their pet food in brick-and

Sample size Number of pet owners who buy their pet food in brick and mortar storms is

1. From a sample of 230 pet owners, 104 indicate that they buy their pet food in brick-and-mortar stores. a. Write the value of the sample statistic to three decimal places, using correct notation. Show your calculation here. b. Define the parameter this sample statistic estimates. I c. An estimate of the standard error for this statistic is 0.03117. Find a 95% confidence interval to three decimal places for the parameter defined here. Show all calculations. d. Interpret the 95% confidence interval in context. e. Which of the following best explains the meaning of 95% confidence in this question? Check only one. The proportion of 95% of all pet owners who buy their pet food in brick-and-mortar stores is in the interval. The proportion of 95% of the pet owners in this sample who buy their pet food in brick-and- mortar stores is in the interval. There is a 95% chance that the proportion of all not own ub bir a

1. From a sample of 230 pet owners, 104 indicate that they buy their pet food in brick-and-mortar stores. a. Write the value of the sample statistic to three decimal places, using correct notation. Show your calculation here. b. Define the parameter this sample statistic estimates. I c. An estimate of the standard error for this statistic is 0.03117. Find a 95% confidence interval to three decimal places for the parameter defined here. Show all calculations. d. Interpret the 95% confidence interval in context. e. Which of the following best explains the meaning of 95% confidence in this question? Check only one. The proportion of 95% of all pet owners who buy their pet food in brick-and-mortar stores is in the interval. The proportion of 95% of the pet owners in this sample who buy their pet food in brick-and- mortar stores is in the interval. There is a 95% chance that the proportion of all not own ub bir a

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 13PPS

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