7.16 How do you position yourself when you are going to sleep? A website tells us...

7.16 How do you position yourself when you are going to sleep? A website tells us that 41% of use start in the fetal position, another 28% start on our side with legs straight, 13% start on their back, and 7% on their stomach. The remaining 11% have no standard starting sleep position. If a random sample of 1000 people produces the frequencies in the table below, should you doubt the proportions given in the article in the website? Show all the details of the test, and use a 5% significance level.

Sleep Position	Frequency
Fetal	391
Side, legs straight	257
Back	156
Stomach	89
None	107
Total	1000

Expert Solution

null hypothesis Ho: proportion of people position in sleep is as stated given in the article in the website

Alternate hypothesis Ho: proportion of people position in sleep is not as stated given in the article in the website

degree of freedom =categories-1=	4
for 0.05 level and 4 degree of freedom :rejection region =		9.488
applying chi square goodness of fit test:

		% *students			pearson
	relative	observed	Expected	residual	Chi square
category	frequency(p)	O_i	E_i=total*p	R²_i=(O_i-E_i)/√E_i	R²_i=(O_i-E_i)²/E_i
Fetal	0.410	391.000	410.0000	-0.94	0.880
Side, legs straight	0.280	257.000	280.0000	-1.37	1.889
Back	0.130	156.000	130.0000	2.28	5.200
Stomach	0.070	89.000	70.0000	2.27	5.157
None	0.110	107.000	110.0000	-0.29	0.082
total	1.000	1000	1000		13.2087

test statistic X² =

13.2087

since test statistic falls in rejection region we reject null hypothesis
we have sufficient evidence to conclude that proportion of people position in sleep is not as stated given in the article in the website

milcah answered 5 months ago

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