The proportions of blood types O, A, B, and AB in the general population of a particular country are known to be in the ratio 49:38:9:4, respectively. A research team, investigating a small isolated community in the country, obtained the following frequencies (i. e. observed number of cases) of blood type. Blood type O A B AB
Frequency 87 59 20 4
Test the hypothesis that the proportions in this community do not differ significantly from those in the general population.

The proportions differ significantly from those in the general population.

Step-by-step explanation:

We state our null and alternative hypotheses as

H0: p1= 49/100, p2= 38/100, p3= 9/100 and p4= 4/100 for a multinomial distribution involving four categories and n= 170

against

Ha: pi≠ pi0 for at least one value of i= 1,2,3,4

The significance level is set at ∝= 0.05

The test statistic under H0 is

χ² = ∑ (Oi- ei)²/ei

which has approximate chi square distribution with 3d.f  (n-1)

Computations: Under H0 the expected frequencies are

np10= Blood type O = 170 * 49/100= 83.3

np20 = Blood type A = 170 * 38/100= 64.6

np30 = Blood type B = 170 * 20/100= 11.76

np40 = Blood type AB = 170 * 4/100= 2.35

The value of χ² is computed as follows

Cell       Observed         Estimated        (Oi-ei)            (Oi-ei)²   (Oi-ei)²/ei

             Frequency      Frequency  

               Oi                    ei

1             87                        83.3               3.7               13.69        0.157

2            59                      64.6              -5.6                 31.36       0.531

3             20                     34                  -14                   196           9.8

4               4                      6.8                -2.8                  7.84         1.96      

∑             170                    188.7                                                  χ²= 12.43  

The critical region is χ²≥ χ²(0.05,3) = 7.82 for alpha = 0.05 and

χ²≥ χ²(0.01,3) = 11.34  for alpha = 0.01

As the calculated value lies in the critical region for both value of alpha we reject our null hypothesis and accept our alternate hypothesis. The proportions differ significantly from those in the general population.

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?

the ratio of grapes to blueberries she should use is 12: 3

step-by-step explanation:

if mandie is making 15 cups of fruit salad, the ratio of grapes to blueberries she should use is 12: 3.