Question

The owner of a local pizzeria has recently surveyed a random sample of n = 30 delivery times. He would now like to determine whether or not the mean delivery time (μ) is less than 20 minutes. Suppose he found that the sample mean time for delivery (X bar) was 17.5 minutes and the sample standard deviation was (s) 6 minutes. Assuming that the level of significance α = 0.05, please answer the following questions. 1. State your null and alternate hypotheses : 2. What is the value of test statistic? Please show all the relevant calculations. 3. What is the rejection criteria based on critical value approach? 4. What is the Statistical decision (i.e. reject /or do not reject the null hypothesis)? Provide justification for your decision.

Answer 1

answer:

given data,

the recently surveyed sample as randomly is 30

the mean is less than 20 minutes

the x bar is 17.5

the standard deviation is 6 minutes

the significance level is 0.05

( 1 )

to find the state of the null and alternative hypothesis....

the hypothesis is below,

this are the hypothesis is writes as the

the null hypothesis is 20 and

the alternative hypothesis is 20

so finally this are the states of the hypothesis.

( 2 )

to find the value of the test statistics is ....

the probability is shown in the below

here we are know as the values is already

now we are known as formula is test x bar - / s / sqrt (n)

now substitute the values in the above formula

17.5 - 20 / 6 / sqrt ( 30 )

       -2.5 / 1.095

   - 2.28310

therefore -2.28310

so finally the test statistic value is - 2.28310

-2.28310

( 3 )

to find the rejection of the critical value is ....

here we are know as the values is

now the sample n is 30, so the df i s 30-1= 29

so finally the df is 29

the critical value t is -1.699

now this are based the above information, the statistics t is rejection criteria , it is the -1.699

so finally the t statistics rejection criteria is less than -1.699

less than -1.699

( 4 )

to find the statistical rejection is ....

the above information based the statistic test value is -2.28310

these are the null hypothesis is will be reject

so finally these are 20 minutes of and significance level is 0.05 as the is will not supported to the mean delivery of that.

NOTE:  these of the answer has as the, i hope this are of the answer is enough, if you need the more information, please comment.

THANK YOU