A biologist is studying the composition of birds on a lake and counts 61 ducks, 17 geese, 11 cranes, 15 swans, and 6 herons. From previous studies performed around the same time of the year, she expects 50% of the birds to be ducks, 23% to be geese, 12% to be cranes, 10% to be swans, and 5% to be herons. What are the correct null and alternative hypotheses for performing a chi-square goodness of fit test

Observed birds

Number of ducks = 61

Number of geese = 17

Number of cranes = 11

Number of swans = 15

Number of herons = 6

Total number of observed birds = 61 + 17 + 11 + 15 + 6 = 110

Expected birds percentage:

ducks = 50%

geese = 23%

cranes = 12%

swans = 10%

herons = 5%

So, count of expected birds according to given percentage:

ducks = 50/100 * total number of birds = 50/100 * 110 = 55

geese = 23/100 * 110 = 25 (approx)

cranes = 12/100 * 110 = 13 (approx)

swans = 10/100 * 110 = 11 (approx)

herons = 5/100 * 110 = 6 (approx)

The chi-square goodness of fit test is used to compare the observed distribution with the expected distributed distribution of the population. In this,

Null hypothesis: There is no significant difference between observed count and expected count

Alternative hypothesis: There is significant difference between observed count and expected count

Step-by-step explanation:

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.