Question

Refer to the Lincolnville School District bus data.

A. Select the variable for the number of miles traveled last month. Conduct a hypothesis test to determine whether the mean miles traveled last month equals 10,000. Use the .01 significance level. Find the p-value and explain what it means.

B. A study of school bus fleets reports that the average per bus maintenance cost is $4,000 per year. Using the maintenance cost variable, conduct a hypothesis test to determine whether the mean maintenance cost for Lincolnville’s bus fleet is more than $4,000 at the .05 significance level. Determine the p-value and report the results.

Please use excel to find results.

Miles	Maintenance Cost
11973	4646
11969	1072
11967	9394
11948	1078
11925	1008
11922	5329
11896	4794
11889	3952
11837	3742
11814	4376
11800	4832
11798	5160
11789	1955
11782	2775
11781	5352
11778	3065
11757	3143
11707	1569
11704	7766
11698	3743
11698	2540
11691	4342
11668	3361
11662	3097
11615	8263
11610	4218
11576	2028
11533	5821
11518	9069
11462	3011
11461	9193
11418	4795
11359	505
11358	2732
11344	3754
11342	4640
11336	8410
11248	5922
11231	4364
11222	3190
11168	3213
11148	4139
11127	3560
11112	3920
11100	6733
11048	3770
11018	5168
11003	7380
10945	3656
10911	6213
10902	4279
10802	10575
10802	4752
10760	3809
10759	3769
10755	2152
10726	2985
10724	4563
10674	4723
10662	1826
10633	1061
10591	3527
10551	9669
10518	2116
10473	6212
10355	6927
10344	1881
10315	7004
10235	5284
10227	3173
10210	10133
10209	2356
10167	3124
10140	5976
10128	5408
10095	3690
10081	9573
10075	2470
10055	6863
10000	4513

Answer 1

A.

Sample mean using excel function AVERAGE(), x̅ = 11120.425

Sample standard deviation using excel function STDEV.S, s = 615.8518

Sample size, n = 80

Null and Alternative hypothesis:

Ho : µ = 10000

H1 : µ ≠ 10000

Test statistic:

t = (x̅- µ)/(s/√n) = (11120.425 - 10000)/(615.8518/√80) = 16.2724

df = n-1 = 79

p-value :

Two tailed p-value = T.DIST.2T(ABS(16.2724), 79) = 0.0000

Decision:

p-value < α, Reject the null hypothesis.

There is not enough evidence to support the claim that the mean miles traveled last month equals 10,000 at 0.01 significance level.

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B.

Sample mean using excel function AVERAGE(), x̅ = 4551.8875

Sample standard deviation using excel function STDEV.S, s = 2331.533108

Sample size, n = 80

Null and Alternative hypothesis:

Ho : µ ≤ 4000

H1 : µ > 4000

Test statistic:

t = (x̅- µ)/(s/√n) = (4551.8875 - 4000)/(2331.5331/√80) = 2.1172

df = n-1 = 79

p-value :

Right tailed p-value = T.DIST.RT(2.1172, 79) = 0.0187

Decision:

p-value < α, Reject the null hypothesis.

There is enough evidence to conclude that the mean maintenance cost for Lincolnville’s bus fleet is more than $4,000 at the .05 significance level.