Based on a smartphone survey, assume that 42% of adults with smartphones use them in theaters. In a separate survey of 259 adults with smartphones, it is found that 106 use them in theaters. a. If the 42% rate is correct, find the probability of getting 106 or fewer smartphone owners who use them in theaters. b. Is the result of 106 significantly low? a. If the 42% rate is correct, the probability of getting 106 or fewer smartphone owners who use them in theaters is (Round to four decimal places as needed.) b. Is the result of 106 significantly low? because the probability of this event is than the probability cutoff that corresponds to a significant event, which is

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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### Smartphone Usage Study: Statistical Analysis

Based on a smartphone survey, assume that 42% of adults with smartphones use them in theaters. In a separate survey of 259 adults with smartphones, it is found that 106 use them in theaters.

#### a. Finding the Probability
If the 42% rate is correct, find the probability of getting 106 or fewer smartphone owners who use them in theaters.

- **Question:** If the 42% rate is correct, the probability of getting 106 or fewer smartphone owners who use them in theaters is (Round to four decimal places as needed):
  - **Answer:** [To be calculated]

#### b. Determining Significance
Is the result of 106 significantly low?

- **Question:** 
  - **Dropdown 1:** Select an appropriate statement regarding the significance.
  - **Textbox:** Calculate the probability.
  - **Dropdown 2:** Choose the probability cutoff that corresponds to a significant event:
    - 0.5
    - 0.95
    - 0.05

#### Analysis of the Results:
1. **Probability Calculation:** 
   - Use statistical techniques (e.g., binomial or normal approximation) to compute the probability.
   - Ensure the value is rounded to four decimal places.

2. **Significance Evaluation:** 
   - Compare the computed probability against standard significance levels (commonly 0.05 or 5%).
   - Determine if the occurrence of 106 smartphone users in theaters is statistically notable.

### Dropdown and Textbox Explanations:
- **Dropdown 1 Options:**
  - "because the probability of this event is lower than the probability cutoff..."
  - "because the probability of this event is higher than the probability cutoff..."

- **Textbox:** 
  - Enter the calculated probability here.

- **Dropdown 2 Options:** 
  - Standard significance thresholds to determine the rarity of the event.

### Notes:
- The dropdown list contains options to assist in evaluating the significance based on the probability.
- The textbox field is for entering the probability value calculated in part (a).
   
### Conclusion:
This exercise demonstrates the application of probability concepts in assessing real-world data scenarios. By calculating and comparing probabilities, students can gain insights into the significance of observed events, fostering a better understanding of statistical principles.
Transcribed Image Text:### Smartphone Usage Study: Statistical Analysis Based on a smartphone survey, assume that 42% of adults with smartphones use them in theaters. In a separate survey of 259 adults with smartphones, it is found that 106 use them in theaters. #### a. Finding the Probability If the 42% rate is correct, find the probability of getting 106 or fewer smartphone owners who use them in theaters. - **Question:** If the 42% rate is correct, the probability of getting 106 or fewer smartphone owners who use them in theaters is (Round to four decimal places as needed): - **Answer:** [To be calculated] #### b. Determining Significance Is the result of 106 significantly low? - **Question:** - **Dropdown 1:** Select an appropriate statement regarding the significance. - **Textbox:** Calculate the probability. - **Dropdown 2:** Choose the probability cutoff that corresponds to a significant event: - 0.5 - 0.95 - 0.05 #### Analysis of the Results: 1. **Probability Calculation:** - Use statistical techniques (e.g., binomial or normal approximation) to compute the probability. - Ensure the value is rounded to four decimal places. 2. **Significance Evaluation:** - Compare the computed probability against standard significance levels (commonly 0.05 or 5%). - Determine if the occurrence of 106 smartphone users in theaters is statistically notable. ### Dropdown and Textbox Explanations: - **Dropdown 1 Options:** - "because the probability of this event is lower than the probability cutoff..." - "because the probability of this event is higher than the probability cutoff..." - **Textbox:** - Enter the calculated probability here. - **Dropdown 2 Options:** - Standard significance thresholds to determine the rarity of the event. ### Notes: - The dropdown list contains options to assist in evaluating the significance based on the probability. - The textbox field is for entering the probability value calculated in part (a). ### Conclusion: This exercise demonstrates the application of probability concepts in assessing real-world data scenarios. By calculating and comparing probabilities, students can gain insights into the significance of observed events, fostering a better understanding of statistical principles.
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