HW Problem 47. (5 pts) Squash is big business in Alabama. One town in the state,

Question

HW Problem 47. (5 pts) Squash is big business in Alabama. One town in the state, Talladega, has a reputation for growing the biggest squash in the state. Not so fast, says rival town Woodstock’s mayor, Tyler Goodson. (Goodson is very excited about this year’s crop of yellow summer squash.) Woodstock has been trying really hard for years to dethrone Talladega as the town with the biggest quash in Alabama and now Goodson believes it’s time to prove it. Consequently, Goodson hires a researcher (at town expense, of course) to confirm his theory. The researcher scours the Woodstock countryside and randomly samples 24 yellow summer squash immediately before harvest. This results in a sample mean weight of 24.5 ounces with a sample standard deviation of 3.4 ounces. 25 such squash are also randomly sampled in Talladega which results in a sample mean weight of 23.1 with a sample standard deviation of 3.6 ounces. At the .05 level of significance, is there enough evidence to confirm Mayor Goodson’s belief that yellow summer squash in Woodstock is larger (in terms of weight) than yellow summer squash in Talladega? List and clearly label all eight steps.

Explanation / Answer

47.

Given that,
mean(x)=24.5
standard deviation , s.d1=3.4
number(n1)=24
y(mean)=23.1
standard deviation, s.d2 =3.6
number(n2)=25
null, Ho: u1 = u2
alternate, H1: u1 > u2
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.714
since our test is right-tailed
reject Ho, if to > 1.714
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =24.5-23.1/sqrt((11.56/24)+(12.96/25))
to =1.4
| to | =1.4
critical value
the value of |t | with min (n1-1, n2-1) i.e 23 d.f is 1.714
we got |to| = 1.39995 & | t | = 1.714
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value:right tail - Ha : ( p > 1.4 ) = 0.08744
hence value of p0.05 < 0.08744,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 > u2
test statistic: 1.4
critical value: 1.714
decision: do not reject Ho
p-value: 0.08744

we do not have enough evidence to support the claim that Mayor Goodson’s belief that yellow summer squash in Woodstock is larger (in terms of weight) than yellow summer squash in Talladega

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