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25.04.2020 •
Mathematics
An article studied differences between expert and consumer ratings by considering medal ratings for wines, which could be gold (G), silver (S), or bronze (B). Three categories were then established.
Rating is the same [(G, G), (B, B), (S, S)]
Rating differs by one medal [(G, S), (S, G), (S, B), (B, S)]
Rating differs by two medals [(G, B), (B, G)]
The observed frequencies for these three categories were 61, 108, and 47, respectively. On the hypothesis of equally likely expert ratings and consumer ratings being assigned completely by chance, each of the nine medal pairs has probability 1/9.
Carry out an appropriate chi-squared test using a significance level of 0.10.
Calculate the test statistic. (Round your answer to two decimal places.)
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Ответ:
test statistic= 1.73
the results are not significant
Step-by-step explanation:
Expected probability of all rating= 1/9 or 0.11111
total number of observations= 61+108+47= 216
Observed value for same rating= 61/216= 0.282407
Observed value for Rating differing by one medal= 108/216= 0.5
Observed value for Rating differing by two medal= 47/216= 0.2175925926
Ch- Squared test: Χ²= Σ (O - E)²/ E
O: observed value
E: Expected value
X²= (0.28241-0.11111)²/ 0.1111 +(0.5-0.11111)²/ 0.1111 + (0.21759-0.11111)²/ 0.1111
X²= 1.727 or 1.73
degrees of freedom= 216-1=215
at 0.1 significance and 215 degress of freedom, p-value is 1.0
The result is not significant as p value is greater than 0.1
Ответ:
First let's find the points of intersection:
x^3=x^2==>x^3-x²=x²(x-1)==>x=0 or x=1
(x²)'=2x
(x^3)'=3x²
If x=0 then y=0*x+0 is a commun tangent of the 2 curves.
==> angle=0°
if x=1 then
tan a=2 and tan b=3
angle=arctan 3-arctan 2=8.130120°