According to a guide, 50% of cell phone users have only one cell number, 36% hav

Question

According to a guide, 50% of cell phone users have only one cell number, 36% have two numbers,12% have three numbers, and 22% have four or more numbers. An independent survey of 953 randomly selected cell phone users found that 469 pay for only one number, 344 pay for two numbers,114 pay for three numbers, and 26 pay for four or more numbers. Conduct a test to determine if the data from the independent survey contradict the percentages reported by the guide. Use alphaequals=0.1.

Determine the null and alternative hypotheses for this test. Choose the correct answer below.

A.

Upper H 0 :H0:

p 1 equals 50 % comma p 2 equals 36 % comma p 3 equals 12 % comma p 4 equals 2 %p1=50%, p2=36%, p3=12%, p4=2%

Upper H Subscript a Baseline :Ha:

At least one of the multinomial probabilities does not equal its hypothesized value.

B.

Upper H 0 :H0:

p 1 equals p 2 equals p 3 equals p 4p1=p2=p3=p4

Upper H Subscript a Baseline :Ha:

p 1 not equals p 2 not equals p 3 not equals p 4p1p2p3p4

C.

Upper H 0 :H0:

p 1 not equals p 2 not equals p 3 not equals p 4p1p2p3p4

Upper H Subscript a Baseline :Ha:

At least one of the multinomial probabilities equals its hypothesized value.

Now find the test statistic.

chi squared2equals= _______

(Round to two decimal places as needed.)

Determine the p-value.

p-valueequals= _______

(Round to four decimal places as needed.)

Choose the correct conclusion below.

A.

Fail to rejectFail to reject Upper H 0H0. There is insufficientinsufficient evidence that the data from the survey contradict the percentages reported by the guide.

B.

RejectReject Upper H 0H0. There is sufficientsufficient evidence that the data from the survey contradict the percentages reported by the guide.

C.

RejectReject Upper H 0H0. There is insufficientinsufficient evidence that the data from the survey contradict the percentages reported by the guide.

D.

Fail to rejectFail to reject Upper H 0H0. There is sufficientsufficient evidence that the data from the survey contradict the percentages reported by the guide.

Explanation / Answer

Given p1 = 0.5, p2 = 0.36, p3 = 0.12 and p4 = 0.02, =0.1, degrees of freedom = n-1 = 4-1 = 3

The Hypothesis: Option A

H0: p1=50%, p2=36%, p3=12%, p4=2%: The data is consistent

Ha: At least one of the multinomial probabilities does not equal its hypothesized value.

The Test Statistic: The table below gives us the value of 2

2 = 2.65 (Rounding to 2 decimal places)

The P value: For 2 = 2.65 for df = 3 is 0.449

The Decision Rule: If P value is < , Then reject H0.

W can also find the critical value(2critical) at = 0.1 for df = 3 = 6.25 and if is 2 > , we reject H0

The Decision: Since the P value (0.449) is > (0.1), Hence we fail to reject H0.

We also see that 2(2.65) is < 2critical(6.25), therefore we fail to reject H0.

The Conclusion: OPTION D

Fail to Reject H0. There is insufficient evidence that the data from the survey contradicts the percentages reported by the guide (It means the data from the 2 are consistent).

Observed Probability Expected O-E (O-E)2 (O-E)2/E 469 50% 476.5 -7.5 56.25 0.118048269 344 36% 343.08 0.92 0.8464 0.002467063 114 12% 114.36 -0.36 0.1296 0.001133263 26 2% 19.06 6.94 48.1636 2.526946485 2 2.64859508

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