Mathematics, 17.03.2020 22:30 PluggedIn

In a random sample of 60 shoppers from a large suburban mall, 36 indicated that they had been to a movie in the past month. In an independent random sample of 50 shoppers chosen from the downtown shopping area, 31 indicated that they had been to a movie in the past month. What significance test should be used to determine whether these data provide sufficient evidence to reject the hypothesis that the proportion of suburban mall shoppers who had been to a movie in the same month is the same as the proportion downtown

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There is no enough statistical evidence to reject the hypothesis that the proportion of suburban mall shoppers who had been to a movie in the same month is the same as the proportion downtown.

Step-by-step explanation:

We have to perform an hypothesis test on the difference of proportions to see if there is enough evidence to reject the null hypothesis.

The null and alternative hypothesis are:

$H_0: \pi_1-\pi_2=0\\\\H_a: \pi_1-\pi_2\neq0$

The significance level is assumed to be α=0.05

The suburban sample has a proportion of

p_1=36/60=0.6

The downtown sample has a proportion of

p_2=31/50=0.62

The average of proportion is:

$p=\frac{n_1p_1+n_2p_2}{n_1+n_2}=\frac{60*0.60+50*0.62}{60+50}=\frac{67}{110}=0.61$

The standard deviation of the difference of proportions is:

$s_{p1-p2}=\sqrt{\frac{p(1-p)}{n_1} +\frac{p(1-p)}{n_2} } =\sqrt{\frac{0.61*0.39}{60} +\frac{0.61*0.39}{50} }\\\\s_{p1-p2}=\sqrt{0.003965+0.004758}=0.0934$

Then, we can calculate the value of the statistic z

$z=\frac{p_1-p_2}{s}=\frac{0.60-0.62}{0.0934}=\frac{-0.02}{0.0934} = 0.214$

The P-value for this z is:

P(|z|0.214)=0.83054

The P-value is bigger than the significance level, so there is no enough evidence to reject the null hypothesis.

Answer from: Quest

The point (5, 10) will work for the rule y=x+5.y= 10 x= 510=5+510=10therefore the ordered pair (5, 10) works for the rule

Answer from: Quest

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺