The mean waiting time at the drive-through of a fast food from the time the order is placed to the time the order is recieved is 84.3 seconds. A manager devises a new drive-through system that he believes will decrease the wait time. To test his claim, he initiates the new system at his restaurant and measures the wait time for 45 randomly selected orders and finds the sample mean to be 81.9 and a sample standard deviation of 17.3. 1. Has the wait time significantly decreased?
2. Write the appropriate hypothesis statements for this test.
3. Also what is the t-test and p-value?

1.) No ;

2.) - 0.931

3.) 0.1785

Step-by-step explanation:

Given :

μ = 84.3 ; xbar = 81.9 ; s = 17.3

H0 : μ = 84.3

H1 : μ < 84.3

The test statistic :

(xbar - μ) ÷ (s/√(n))

(81.9 - 84.3) / (17.3/√45)

-2.4 / 2.5789317

= - 0.9306

= - 0.931

Using the test statistic, we could obtain the Pvalue : df = n - 1 ; df = 45 - 1 = 44

Using the Pvalue calculator :

Pvalue(-0.9306, 44) = 0.1785

Using α = 0.05

The Pvalue > α

Then we fail to reject H0; and conclude that there is no significant evidence to support the claim that the mean waiting time is less than 84.3

n

step-by-step explanation:

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 ☺