4 In one month, the national mean price per gallon (in dollars) of gasoline was

Question

4 In one month, the national mean price per gallon (in dollars) of gasoline was 3.107. The 3.05 307 311 3 08 data table here represents a random sample of 20 gas stations in city A. Is gas in city A more expensive than the nation? Assume the data 3.13 3.16 3.16 3.18 come from a normal population with no outliers. Complete parts (a) through (d) below 323 323 3.23 325 6 3.14 3.13 3.12 3.15 3.21 3.23 3.22 323 10 Complete parts (a) through (d) below 12 13 14 15 16 17 18 19 20 21 (a) What type of test should be used? O O O A hypothesis test regarding a single population mean using Student's approximate t A hypothesis test regarding two population standard deviations A hypothesis test regarding the difference between two population proportions from independent samples using the standard normal test statistic O A hypothesis test regarding the difference of two means using a matched-pairs design (b) Determine the null and alternative hypotheses H1 Type integers or decimals.) (c) Use technology to calculate the P-value (Round to three decimal places as needed) (d) Draw a conclusion based on the hypothesis test Choose the correct answer below 23 24 25 26 27 28 29 30 31 Click to select your answer(s). 32

Explanation / Answer

a.
A hypothesis regarding a single population mean using student approximate 1
b.
Given that,
population mean(u)=3.107
sample mean, x =3.1625
standard deviation, s =0.0674
number (n)=20
null, Ho: =3.107
alternate, H1: >3.107
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.729
since our test is right-tailed
reject Ho, if to > 1.729
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =3.1625-3.107/(0.0674/sqrt(20))
to =3.6825
| to | =3.6825
critical value
the value of |t | with n-1 = 19 d.f is 1.729
we got |to| =3.6825 & | t | =1.729
make decision
hence value of | to | > | t | and here we reject Ho
p-value :right tail - Ha : ( p > 3.6825 ) = 0.00079
hence value of p0.05 > 0.00079,here we reject Ho
ANSWERS
---------------
b.
null, Ho: =3.107
alternate, H1: >3.107
test statistic: 3.6825
critical value: 1.729
decision: reject Ho
c.
p-value: 0.00079
d.
although no level of significance is stated ,the p-value is so small null can be rejected hypothesis.there is evidence to support that gas prices of A more that national average

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