An economist studying fuel costs suspected that the mean price of gasoline in her state was more than\$3

$3

dollar sign, 3

per gallon on a certain day. On that day, she sampled40

40

40

gas stations to testH_0: \mu=\$3

H0

:=$3

H, start subscript, 0, end subscript, colon, mu, equals, dollar sign, 3

versusH_\text{a}: \mu>\$3

Ha

:>$3

H, start subscript, start text, a, end text, end subscript, colon, mu, is greater than, dollar sign, 3

, where\mu

mu

is the mean price of gasoline per gallon that day in her state.

The sample data had a mean of\bar x=\$3.04

x

=$3.04

x, with, \bar, on top, equals, dollar sign, 3, point, 04

and a standard deviation ofs_x=\$0.39

sx

=$0.39

s, start subscript, x, end subscript, equals, dollar sign, 0, point, 39

. These results produced a test statistic oft\approx0.65

t0.65

t, approximately equals, 0, point, 65

and a P-value of approximately0.260

0.260

0, point, 260

.

Assuming the conditions for inference were met, what is an appropriate conclusion at the\alpha=0.01

=0.01

alpha, equals, 0, point, 01

significance level?