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SSSSS [86.1K]
4 years ago
13

A business school professor uses multiple choice tests. Each question on his exams has five possible answers which are assumed t

o be equally likely. One of his brighter students wants to know whether this assumption is correct and whether or not this professor randomly distributes the correct answer over the five choices. If not, he believes he can improve his odds when guessing the answer to questions he is not sure of. The student took 1000 questions from previous tests and found the following distribution: a = 185, b = 230, c = 215, d = 180 and e = 190.
Required:
a. Formulate the null hypothesis for this test?
b. How many degrees of freedom do you have for this test?
c. What is the calculated value of the test statistic?
Mathematics
1 answer:
avanturin [10]4 years ago
7 0

Answer:

a. The null hypothesis for this test is that the observed distribution is the same as uniform distribution

b. The degrees of freedom do you have for this test is 4

c.  The calculated value of the test statistic is 9.250

Step-by-step explanation:

a. According to the given data we can conclude that the null hypothesis for this test is that the observed distribution is the same as uniform distribution.

b. In order to calculate the degrees of freedom do you have for this test we would have to make the following calculation:

degrees of freedom=k-1

degrees of freedom=5-1

degrees of freedom=4

c. In order to calculate the value of the test statistic first we have to calculate the frecuency expected as follows:

expected frecuency=total observed frecuency/total number of category

expected frecuency=1,000/5

expected frecuency=200

Hence, to calculate the value of the test statistic we have to calculate the following formula:

x∧2=∑(fo-fe)∧2/fe

=(185-200)∧2/200+(230-200)∧2/200+(215-200)∧2/200+(180-200)∧2+(190-200)∧2

=9.250

The calculated value of the test statistic is 9.250

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Dons signature coffee blend is 60% dark roast and 40% light roast. He has 10 kg of blend A, which is 80% dark roast and 20% ligh
astraxan [27]

Answer

Find out the how many kilograms of blend A will don need to use to make 10 kg of his signature blend .

To proof

As given

Dons signature coffee blend is 60% dark roast and 40% light roast.

He has 10 kg

60 % is written in the decimal form

= \frac{60}{100}

= 0.6

40 % is written in the decimal form

= \frac{40}{100}

= 0.4

Now 60% dark roast of  10 kg = 0.6 ×10

                                                 = 6 kg

Now 40% of  10 kg = 0.4 × 10

                               = 4 kg

As given

He has 10 kg of blend A, which is 80% dark roast and 20% light roast  i.e 80% of the 6kg is dark roast and 20% of the  4kg is light roast .

80% is written in the decimal form

= \frac{80}{100}

= 0.8

80% of the 6kg is dark roast = 0.8 × 6

                                                = 4.8 kg

20% is written in the decimal form

= \frac{20}{100}

= 0.2

20% of the 4kg is light roast = 0.2 × 4

                                               = .8kg

Total kilograms of blend A will don need to use to make 10 kg of his signature blend =  4.8 kg + .8 kg

                          = 5.6 kg

Hence proved




 


8 0
3 years ago
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