Q2. (17 points) A producer of ready-made pumpkin pies sells their pie by the oun

Question

Q2. (17 points) A producer of ready-made pumpkin pies sells their pie by the ounce. The pie should weigh approximately 24 ounces. For quality assurance they weigh a random sample of 20 pies from each batch to see whether there is evidence the average weight of the batch of pies is different than 24 ounces. If there is evidence they will need to price the whole batch of pies at a discount and investigate their pie making procedures. From one batch the average weight of the sampled pies is 23.3 ounces with a sample standard deviation of 1.8 ounces. They assume the population of pie weights is normally distributed. Use a significance level of 0.05 to answer the following question of interest.

1.) State: Is there evidence the true average weight of the pumpkin pies is different than 24 ounces?

2.) Plan:

      a. (2 points) State the null and alternative hypotheses to answer the question of interest.

b. (2 points) What type of test is appropriate to answer the question of interest and why?

c. (1 point) State the level of significance.

Explanation / Answer

Given that,
population mean(u)=24
sample mean, x =23.3
standard deviation, s =1.8
number (n)=20
null, Ho: =24
alternate, H1: !=24
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.093
since our test is two-tailed
reject Ho, if to < -2.093 OR if to > 2.093
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =23.3-24/(1.8/sqrt(20))
to =-1.739
| to | =1.739
critical value
the value of |t | with n-1 = 19 d.f is 2.093
we got |to| =1.739 & | t | =2.093
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != -1.7392 ) = 0.0982
hence value of p0.05 < 0.0982,here we do not reject Ho
ANSWERS
---------------
null, Ho: =24
alternate, H1: !=24
test statistic: -1.739
critical value: -2.093 , 2.093
decision: do not reject Ho
p-value: 0.0982

we don't have evidence that the true average weight of the pumpkin pies is different than 24 ounces

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