A consumer group claims that the mean minimum time it takes for a sedan to travel a quarter mile is greater than 14.8 seconds. A random sample of 24 sedans has a mean minimum time to travel a quarter mile of 15.5 seconds and a standard deviation of 2.08 seconds. At α=0.10 is there enough evidence to support the consumer​ group's claim? Complete parts​ (a) through​ (d) below. Assume the population is normally distributed.

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23.

A consumer group claims that the mean minimum time it takes for a sedan to travel a quarter mile is greater than
14.8
seconds. A random sample of
24
sedans has a mean minimum time to travel a quarter mile of
15.5
seconds and a standard deviation of
2.08
seconds. At
α=0.10
is there enough evidence to support the consumer​ group's claim? Complete parts​ (a) through​ (d) below. Assume the population is normally distributed.
 
 
 
​(a) Identify the claim and state
H0
and
Ha.
 
H0: 
muμ
 
less than or equals≤
 
14.814.8
Ha: 
muμ
 
greater than>
 
14.814.8
​(Type integers or decimals. Do not​ round.)
 
The claim is the
alternative
 
hypothesis.
​(b) Use technology to find the​ P-value. Find the standardized test​ statistic, t.
 
t=1.651.65
​(Round to two decimal places as​ needed.)
Obtain the​ P-value.
 
P=0.0560.056
​(Round to three decimal places as​ needed.)
​(c) Decide whether to reject or fail to reject the null hypothesis.
 
 
Reject
Fail to reject
H0
because the​ P-value
 
is
is not
greater than a
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