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: 20¢; 75¢; 50¢; 65¢; 30¢; 55¢; 40¢; 40¢; 30¢; 55¢; $1.50; 40¢; 65¢; 40¢. Assume the underlying distribution is approximately normal.Construct a 95% confidence interval for the population mean worth of coupons .What is the lower bound? ( Round to 3 decimal places )What is the upper bound? ( Round to 3 decimal places )What is the error bound? (Round to 3 decimal places)

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Asked Nov 18, 2019
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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: 20¢; 75¢; 50¢; 65¢; 30¢; 55¢; 40¢; 40¢; 30¢; 55¢; $1.50; 40¢; 65¢; 40¢. Assume the underlying distribution is approximately normal.

Construct a 95% confidence interval for the population mean worth of coupons .

What is the lower bound? ( Round to 3 decimal places )

What is the upper bound? ( Round to 3 decimal places )

What is the error bound? (Round to 3 decimal places)

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Expert Answer

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Step 1

From the given data, one of the data value is in dollars. So, first convert it into cents. That is, $1.50 = 150 cents.

Step-by-step procedure to find sample mean, standard deviation and sample size using Excel:

  • In Excel sheet, enter Data in one column.
  • In Data, select Data Analysis and Choose Descriptive Statistics.
  • In Input Range, select Data and click Labels in First Row.
  • Select Summary Statistics.
  • Click OK.

Output using Excel is shown below:

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Data Mean 53.92857143 Standard Error 8.454444365 Median 45 Mode 40 Standard Deviation 31.63363421 Sample Variance 1000.686813 Kurtosis 6.8581259 Skewness 2.328846225 Range 130 Minimum 20 Maximum 150 Sum 755 Count 14

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Step 2

From the output, the sample mean, standard deviation and sample size are 53.93, 31.63 and 14, respectively.

The formula for finding confidence interval for population mean is shown below:

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CI tt = x +Error bound

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Step 3

For 95% confidence level, the value of tα/2 = t0.05/2 at 13 (=14–1) degrees of freedom using t ...

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31.63 CI 53.93 2.160 x V14 =53.93 t18.260 (35.670,72.190)

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