The monthly incomes for 12 randomly selected​ people, each with a​ bachelor's degree in​ economics, are shown on the right. Complete parts​ (a) through​ (c) below and construct a 95\% confidence interval for the population mean \mu.

UkusakazaL

UkusakazaL

Answered question

2021-07-31

The monthly incomes for 12 randomly selected​ people, each with a​ bachelor's degree in​ economics, are shown on the right. Complete parts​ (a) through​ (c) below.
Assume the population is normally distributed.
a) Find the sample mean.
b) Find the sample standard deviation
c) Construct a 95% confidence interval for the population mean μ. A 95% confidence interval for the population mean is
4450.424596.964366.464455.624151.523727.774283.264527.944407.683946.494023.614221.73

Answer & Explanation

UkusakazaL

UkusakazaL

Beginner2021-08-06Added 1 answers

Step 1
XXX¯(XX¯)24450.42187.129235017.334596.9633.6692111335.14366.46103.169210643.884455.65192.359237002.054151.52111.77112492.723727.77535.521286782.64283.2619.96917398.76764527.94264.649270039.184407.68144.389220848.233946.49316.801100362.84023.61239.68157446.94221.7341.56081727.303Total=51159.49Total=744096.8
Step 2
a) Sample mean:
x=Xn
=51159.4912
=4263.291
The sample mean is 4263.291
Step 3
b) Sample Standard Deviation
sd=(XX)2n1
=744096.8121
=260.087
The sample standard deviation is 260.087
Step 4
c) 95% Confidence Interval for Population mean:
x±tn1×sdn
4263.291±2.201×260.08712
4263.291±165.253
(4098.038, 4428.544)
95% confidence interval for the population mean is (4098.038, 4428.544)

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