Question

STATISTICS HELP!

A shipping company claims that the average delivery time for its next day shipping service is 22 hours. However a group of customers believe that the mean delivery time is longer than 22 hours. Suppose that a random sample of 78 next day deliveries by the company yields a mean delivery time of 23.5 hours, with a standard deviation of 4.8 hours.

a) State the null and the alternative hypotheses to the company's claim

b) Find the value of the test statistic. Round to TWO decimal places

c) What is the p-value? Round to THREE decimal places

Answer 1

null has equality to it, alt doesnt.

what do you believe should they be?

Answer 2

Ho <= 22 hrs
Ha > 22 hrs

seems fair eh?

Answer 3

I have no idea how to even begin the problem lol @amistre64

Answer 4

well the hypothesis are what we want to test. one claims 22 hours, the other claims more than 22 hours so those have to be our hypots

Answer 5

the test stat is then a comparison of the sample mean against the null mean to see if its value is within an acceptable range

Answer 6

assume the null is true and see how far off the sample mean is from it using a modified deviation (sigma/sqrt(n))

Answer 7

But why do we assume that it is true?

Answer 8

its the hypothesis that we either what to reject or fail to reject so its the basis by which to determine if the sample data fits into it

Answer 9

spose my hypothesis is that all baseballs are made of wood, and i find a baseball made of glass. do i assume all baseballs are glass as the basis of my comparison?

Answer 10

No! So thats why you reject it?

Answer 11

the basis of comparison is assuming the null is true and then finding enough evidence (the sample data) to determine if its a worthwhile assumption.

Answer 12

So in this situation I'm assuming that the next day shipping takes 22 hours?

Answer 13

correct, and then see how the sample data of 23.5 fits into the meme

Answer 14

so do you recall your formula for finding a z value?

Answer 15

I'm not sure my teacher told me to always assume u=k or something lol

Answer 16

the null hypot by convention always includes an equality aspect of it.

if we assume Ho = k the Ha not= k and we have a two tailed test
if we want to know if Ha is < or > then k we have a one tailed test

Answer 17

in this case, we want to know if the alternative is greater than 22

Answer 18

in your material it should say something to the effect that the mean of the sample means is normally distributed, with a standard deviation defined as 'standard error' of the means.

when finding the relative measure between the mean of a normal distribution and one of its data points we normally have the formula:

\[z=\frac{x-\bar x}{\sigma}\]

Answer 19

but the standard error (the standard deviation of the distribution of sample means) is not sigma, its sigma/sqrt(n) for a sample size of n

Answer 20

Okay now this is where I get confused .. okay so i'm assuming that the 22 hours is true.
So in order to state the null and alternative hypot I have to always assume u=k?

Answer 21

\[\hat z=\sqrt{n}~\frac{x-\bar x}{\sigma}=\frac{x-\bar x}{\sigma/\sqrt{n}}\]

Answer 22

null is simply the average delivery time is equal to or less than 22 hours

the alternative to this is that the average delivery time is more than 22 hours.

Answer 23

Ho: u <= 22 hrs
Ha: u > 22 hrs

Answer 24

this is the notes my teacher used to help us its kind of similar to what your saying

Answer 25

i dont have msoffice to open that file with on this computer

Answer 26

now we would expect that for any given sample, that its possible to find one or more that dont reflect the actual mean of a population. but we would expect that the majority of the sample means to be within what, 95% of the true mean. 5% is the benchmark for outliers.

Answer 27

23.5 - 22 = 1.5 divided by the standard error of (4.8/sqrt(78))

1.5sqrt(78)/4.8 = 2.7599...

Answer 28

now here is where we start thinking. we assume our sample to be within the normal error range from the true population mean, so under this assumption 23.5 would not be an off the wall result and would be well within what we consider a normal (95%) range of the sample means that we would expect. right?

Answer 29

So would the claim be Ho: u(ge)22 Ha: u>22 hours ?

Answer 30

Ho (another way of writing null hypothesis) is <= 22 .. not (ge) >=

Answer 31

http://www.ltcconline.net/greenl/courses/201/hyptest/hypmean.htm

this looks readable to me

Answer 32

why cant i understand this =((((( I appreciate your help!! Thank you so much but i just dont think i understand statistics

Answer 33

i think your thinking abot it too hard :)

Ho and Ha have to be testable so they must by necessity be different from one another.

we know that the information given has a claim in it that the delivery time is greater than 22, so let this be the Ha

that leaves the rest of the results to be the null hypot, everything that is equal to or less than 22

Answer 34

if your course says Ho = 22 thats fine as well i spose. its just not what i was taught is all

Answer 35

once we have hypothesis to play with, the nest thing to do is to see how well the sample data is going to play with them.

Answer 36

the statistic that we test that by (the test statistic) is then computed the usual way but using the 'standard error' instead of the 'standard deviation' simply becuase we are comparing the distribution of sample means and not the sample data itself and need a different name for it as to avoid any confusion.

Answer 37

Okay now I understand it a little bit better! it makes since that the 22 is equal to Ha because we can reject Ho but not Ha?

Answer 38

we can either 'reject' Ho, or we can 'fail to reject' Ho

we know nothing really about Ha other than it is some other possibility.

We are testing Ho specifically for what it is claiming to be and then either rejecting it if the data doesnt support it, or we fail to reject it if the data is not sufficient to reject it.

Answer 39

spose we make a claim, most M&Ms are green

now, we can either reject this by showing that the data does not support the claim, or we can fail to reject it (but not actually accept it) if the data we present is simply not evidence enough to support someting else

Answer 40

spose we get a sample of M&Ms that are mostly green. this may have happened by sheer coincidence and we simply do not want to put the fate of our hard work and studies into the results of a chance encounter.

Answer 41

this is what is called type 1 and 2 errors in your material. we want to reduce the errors so that we can be x% confident in the results .... but we are never 100% confident.

Answer 42

http://www.kean.edu/~fosborne/bstat/07amean.html

heres another page that covers the same content that i have been trying to relate