The monthly auto insurance premiums in dollars of a sample o

The monthly auto insurance premiums, in dollars, of a sample of 3 types of automobiles are given in the table. (You may assume that all samples are simple random samples.)

b. Use the sign test to test the claim that the median monthly insurance premium for an SUV is greater than $65. Use .05 significance.

c. Use the sign test to test the claim that the median monthly insurance premium for an SUV is less than $65. Use .05 significance.

SUV	63	59	70	60	65	58	61	63	64	61
Compact	71	73	65	72	77	83	77
Truck	52	57	91	61	53	65	72

We can do sign test using MINITAB.

The hypothesis for the test is,

H0 : Median monthly insurance premium for an SUV is $65.

H1 : Median monthly insurance premium for an SUV is greater than $65.

alpha = level of significance. = 0.05

The steps in MINITAB are,

START --> STAT --> Nonparametrics --> 1-sample sign --> variables : SUV --> Confidence level = 95.0 --> test median : 65 --> alternative : greator than --> ok.

These steps will gives us following output.

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Sign Test for Median: SUV

Sign test of median = 65.00 versus > 65.00

N Below Equal Above P Median
SUV 10 8 1 1 0.9980 62.00

Here P-value = 0.9980

but the alternative is right sided .

P-value = 1 - 0.9980 = 0.002

P-value < 0.05

Reject H0 at 5% level of significance.

Conclusion : The median monthly insurance premium for an SUV is greater than $65.

The hypothesis for the test is,

H0 : Median monthly insurance premium for an SUV is $65.

H1 : Median monthly insurance premium for an SUV is less than $65.

Same steps we are do as first.

The steps in MINITAB are,

START --> STAT --> Nonparametrics --> 1-sample sign --> variables : SUV --> Confidence level = 95.0 --> test median : 65 --> alternative : less than --> ok.

These steps will gives us following output.

Sign Test for Median: SUV

Sign test of median = 65.00 versus < 65.00

N Below Equal Above P Median
SUV 10 8 1 1 0.0195 62.00

P-value = 0.0195

P-value < 0.05

Reject H0 at 5% level of significance.

Conclusion : Median monthly insurance premium for an SUV is less than $65.