Question

The display provided from technology available below results from using data for a smartphone​ carrier's data speeds at airports to test the claim that they are from a population having a mean less than 5.00 Mbps. Conduct the hypothesis test using these results. Use a 0.05 significance level. Identify the null and alternative​ hypotheses, test​ statistic,P-value, and state the final conclusion that addresses the original claim.

Answer 1

Assumed data,
sample mean, x =4
standard deviation, s =0.5
number (n)=10 because not given in the data,
Given that,
population mean(u)=5
null, Ho: μ=5
alternate, H1: μ<5
level of significance, α = 0.05
from standard normal table,left tailed t α/2 =1.833
since our test is left-tailed
reject Ho, if to < -1.833
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =4-5/(0.5/sqrt(10))
to =-6.3246
| to | =6.3246
critical value
the value of |t α| with n-1 = 9 d.f is 1.833
we got |to| =6.3246 & | t α | =1.833
make decision
hence value of | to | > | t α| and here we reject Ho
p-value :left tail - Ha : ( p < -6.3246 ) = 0.00007
hence value of p0.05 > 0.00007,here we reject Ho
ANSWERS
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null, Ho: μ=5
alternate, H1: μ<5
test statistic: -6.3246
critical value: -1.833
decision: reject Ho
p-value: 0.00007
we have enough evidence to support the claim that they are from a population having a mean less than 5.00 Mbps.