A local brewery produces three premium lagers named Half Pint, XXX, and Dark Night. Of its premium lagers, they bottle 40% Half Pint, 40% XXX, and 20% Dark Night lagers. In a marketing test of a sample of consumers, 27 preferred the Half Pint lager, 29 preferred the XXX lager, and 24 preferred the Dark Night lager. Using a chi-square goodness-of-fit test, decide to retain or reject the null hypothesis that production of the premium lagers matches these consumer preferences using a 0.05 level of significance. State the value of the test statistic. (Round your answer to two decimal places.) $ \chi_{obt}^2 $

reject the null hypothesis

Step-by-step explanation:

Total observation = 27+49+24 = 100

Expected Frequency :

Half Pint = 100 × 0.4 = 40

XXX = 100 × 0.4 = 40

Dark night = 100 × 0.2 = 20

The Chi-square goodness-of-fit test can be computed as follows:

             Observed              Expected                  

            Frequency(O)         Frequency (E)

Half-       27                            40                                 4.225      

Pint

XXX       29                           40                                  3.025

Dark-       24                          20                                  0.8

night

Total      100                         100                                 8.05

The test statistics = 8.05

8.05

degree of freedom = n -1

degree of freedom =  3 - 1

degree of freedom =  2

The p-value can be computed by using the EXCEL FORMULA (=CHIDIST(8.05,2)

p-value = 0.01786

Since the p-value is less than the level of significance, we reject the null hypothesis

Also using the critical value approach from the EXCEL FUNCTION;

critical chi-square  (=CHIINV(0.05,2) = 5.99

, therefore, we reject the null hypothesis

tickets for the harlem globetrotters

show at michigan state university in

2010 cost $16, $23, or, for vip seats, $40.

total revenue = 16x + 23y + 40z

if 9 times as many $16 tickets were sold

as vip tickets,

x = 9z => x – 9z = 0, if 9 times as many $16 tickets were sold

as vip tickets,

x = 9z => x – 9z = 0, sales of all three kinds of tickets would

total $46,575.

16x + 23y + 40z = 46575, how many of each kind of ticket would

have been sold?

solve for x, y and z

x − 9z = 0

x − y − z = 55

16x + 23y + 40z = 46575

x = 1170

y = 985

z = 130

welcome!

the total estimated nappy use.=10,500,000

step-by-step explanation:

given that on an average the average baby uses 3528 napkins.

in a particular year 2014, the number of births were 299697 in new south wales.

rounding off the number of births to the nearest hundred thousand we have

no of birtsh = 300000

also rounding off the average usage to nearst thousand we get

average use of a baby = 3500

hence total number of nappy estimated to be used = 3500x300000

= 10,500,000

answer is 10,500,000 nappies