Question

Asked Nov 23, 2019

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In a survey, 20 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $40.3 and standard deviation of $5.8. Estimate how much a typical parent would spend on their child's birthday gift (use a 95% confidence level). Give your answers to 3 decimal places.

Express your answer in the format of ¯xx¯ ±± E.

$ ±± $

Step 1

Introduction

The 100 (1 – *α*) % confidence interval for the population mean, *μ*, for given sample standard deviation, *s* is: (*x̅* – (*t _{α}*

Here, *n* is the sample size, *x̅* is the sample mean, and *t _{α}*

The *t*-distribution is used, because the population standard deviation is unknown and the sample standard deviation is being used as a substitute.

Step 2

**Calculation:**

Here, *n* = 20; *x̅* = 40.3; *s* = 5.8.

Therefore, degrees of freedom = *20* – 1 = 19.

Again, 100 (1 – *α*) % = 95% = 0.95.

Thus, *α* = 0.05.

From the Excel formula: =T.INV.2T(0.05,19), *tα*/2; *n* – 1 = *t*0.025; 19 = 2.093.

Thus, the confidence interval is calculated as follows:

(*x̅* – (*tα*/2...

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