A survey of the mean number of cents off that coupons give was conducted by randomly surveying one coupon per page from the coupon sections of a recent San Jose Mercury News. The following data were collected: 25; 70; 45; 65; 30; 55; 40; 40; 30; 55; $1.50; 40; 65; 40. Assume the underlying distribution is approximately normal.NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)Part (a)(i) Round your answer to two decimal places.x = ¢(ii) Round your answer to two decimal places.sx = ¢(iii) Enter an exact number as an integer, fraction, or decimal.n = (iv) Enter an exact number as an integer, fraction, or decimal.n − 1 = Which distribution should you use for this problem? (Enter your answer in the form z or tdf where df is the degrees of freedom.) Construct a 95% confidence interval for the population mean worth of coupons.(i) State the confidence interval. (Round your answers to two decimal places.) ¢, ¢ (ii) Sketch the graph.(iii) Calculate the error bound. (Round your answer to two decimal places.)If many random samples were taken of size 14, what percent of the 95% confidence intervals constructed should contain the population mean worth of coupons? %

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Description: A survey of the mean number of cents off that coupons give was conducted by randomly surveying one coupon per page from the coupon sections of a recent San Jose Mercury News. The following data were collected: 25; 70; 45; 65; 30; 55; 40; 40; 30; 55;

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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A survey of the mean number of cents off that coupons give was conducted by randomly surveying one coupon per page from the coupon sections of a recent San Jose Mercury News. The following data were collected: 25; 70; 45; 65; 30; 55; 40; 40; 30; 55; $1.50; 40; 65; 40. Assume the underlying distribution is approximately normal.

NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

Part (a)

(i) Round your answer to two decimal places.

x =  ¢

(ii) Round your answer to two decimal places.

s_x =  ¢

(iii) Enter an exact number as an integer, fraction, or decimal.

n =

(iv) Enter an exact number as an integer, fraction, or decimal.

n − 1 =

Which distribution should you use for this problem? (Enter your answer in the form z or t_df where df is the degrees of freedom.)

Construct a 95% confidence interval for the population mean worth of coupons.
(i) State the confidence interval. (Round your answers to two decimal places.)

  ¢,  ¢

(ii) Sketch the graph.

(iii) Calculate the error bound. (Round your answer to two decimal places.)

If many random samples were taken of size 14, what percent of the 95% confidence intervals constructed should contain the population mean worth of coupons?
%

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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