According to a guide, 47% of cell phone users have only one cell number, 31% have two numbers, 8% have three numbers, and 14% have four or more numbers. An independent survey of 935 randomly selected cell phone users found that 464 pay for only one number, 331 pay for two numbers, 113 pay for three numbers, and 27 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 a = 0.01. Determine the null and alternative hypotheses for this test. Choose the correct answer below. O A. Ho: P1 = P2 = P3 = P4 Hạ: P1 # P2 # P3 # P4 O B. Ho: P1 # P2 # P3 # P4 Ha: At least one of the multinomial probabilities equals its hypothesized value. С. Но: ра 347%, рә %3D 31%, р3 3 8%, ра 3 14% Ha: At least one of the multinomial probabilities does not equal its hypothesized value. Now find the test statistic. x² = |(Round to two decimal places as needed.)

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please find the X^2 and the P-value at a=0.01

### Hypothesis Testing for Multinomial Probabilities

According to a guide, 47% of cell phone users have only one cell number, 31% have two numbers, 8% have three numbers, and 14% have four or more numbers. An independent survey of 935 randomly selected cell phone users found that 464 pay for only one number, 331 pay for two numbers, 113 pay for three numbers, and 27 pay for four or more numbers. Conduct a test to determine if the data from the independent survey contradicts the percentages reported by the guide. Use \( \alpha = 0.01 \).

#### Determine the Null and Alternative Hypotheses for this Test

Choose the correct answer below:

- **A.** \( H_0: p_1 = p_2 = p_3 = p_4 \)
  \( H_a: p_1 \neq p_2 \neq p_3 \neq p_4 \)

- **B.** \( H_0: p_1 \neq p_2 \neq p_3 \neq p_4 \)
  \( H_a: At least one of the multinomial probabilities equals its hypothesized value. \)

- **C.** \( H_0: p_1 = 47\%, p_2 = 31\%, p_3 = 8\%, p_4 = 14\% \)
  \( H_a: At least one of the multinomial probabilities does not equal its hypothesized value. \) 

   ![correct answer check mark next to option C](https://upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Check_mark.svg/2000px-Check_mark.svg.png)

#### Now Find the Test Statistic

\[ \chi^2 = \boxed{\begin{array}{c}\end{array}} \quad (\text{Round to two decimal places as needed.}) \]
Transcribed Image Text:### Hypothesis Testing for Multinomial Probabilities According to a guide, 47% of cell phone users have only one cell number, 31% have two numbers, 8% have three numbers, and 14% have four or more numbers. An independent survey of 935 randomly selected cell phone users found that 464 pay for only one number, 331 pay for two numbers, 113 pay for three numbers, and 27 pay for four or more numbers. Conduct a test to determine if the data from the independent survey contradicts the percentages reported by the guide. Use \( \alpha = 0.01 \). #### Determine the Null and Alternative Hypotheses for this Test Choose the correct answer below: - **A.** \( H_0: p_1 = p_2 = p_3 = p_4 \) \( H_a: p_1 \neq p_2 \neq p_3 \neq p_4 \) - **B.** \( H_0: p_1 \neq p_2 \neq p_3 \neq p_4 \) \( H_a: At least one of the multinomial probabilities equals its hypothesized value. \) - **C.** \( H_0: p_1 = 47\%, p_2 = 31\%, p_3 = 8\%, p_4 = 14\% \) \( H_a: At least one of the multinomial probabilities does not equal its hypothesized value. \) ![correct answer check mark next to option C](https://upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Check_mark.svg/2000px-Check_mark.svg.png) #### Now Find the Test Statistic \[ \chi^2 = \boxed{\begin{array}{c}\end{array}} \quad (\text{Round to two decimal places as needed.}) \]
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