Questions: Streaming video: A streaming service is considering raising its fees. A marketing executive at the company surveys a sample of 415 subscribers and asks them whether they would continue subscribing if fees were raised by 20%. A total of 25 of the 415 replied that they would continue subscribing. The marketing executive of the company claims that less than 10% of all its subscribers would continue subscribing. Can you conclude that the executive's claim is true? Use the alpha=0.01 level of significance and the P-value method with the table. Part: 0 / 5 Part 1 of 5 State the appropriate null and alternate hypotheses. H0: p=0.10 H1: p<0.10 This hypothesis test is a (Choose one) test. - right-tailed - left-tailed - two-tailed

Streaming video: A streaming service is considering raising its fees. A marketing executive at the company surveys a sample of 415 subscribers and asks them whether they would continue subscribing if fees were raised by 20%. A total of 25 of the 415 replied that they would continue subscribing. The marketing executive of the company claims that less than 10% of all its subscribers would continue subscribing. Can you conclude that the executive's claim is true? Use the alpha=0.01 level of significance and the P-value method with the table.

Part: 0 / 5

Part 1 of 5

State the appropriate null and alternate hypotheses.

H0: p=0.10
H1: p<0.10

This hypothesis test is a (Choose one) test.
- right-tailed
- left-tailed
- two-tailed

Transcript text: Streaming video: A streaming service is considering raising its fees. A marketing executive at the company surveys a sample of 415 subscribers and asks them whether they would continue subscribing if fees were raised by $20 \%$. A total of 25 of the 415 replied that they would continue subscribing. The marketing executive of the company claims that less than $10 \%$ of all its subscribers would continue subscribing. Can you conclude that the executive's claim is true? Use the $\alpha=0.01$ level of significance and the $P$-value method with the table. Part: $0 / 5$ Part 1 of 5 State the appropriate null and alternate hypotheses. \[ \begin{array}{l} H_{0}: p=.10 \\ H_{1}: p<.10 \end{array} \] This hypothesis test is a (Choose one) test. right-tailed left-tailed two-tailed

Solution

Solution Steps

Step 1: State the Hypotheses

We are testing the following hypotheses: \[ \begin{align_} H_{0}: & \quad p = 0.10 \\ H_{1}: & \quad p < 0.10 \end{align_} \]

Step 2: Calculate the Test Statistic

The test statistic $ Z $ is calculated using the formula: \[ Z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}} \] Substituting the values: \[ \hat{p} = \frac{25}{415} \approx 0.0602, \quad p_0 = 0.10, \quad n = 415 \] Calculating $ Z $: \[ Z = \frac{0.0602 - 0.10}{\sqrt{\frac{0.10(1 - 0.10)}{415}}} \approx -2.6998 \]

Step 3: Determine the P-value

The P-value associated with the test statistic $ Z = -2.6998 $ is: \[ \text{P-value} = 0.0035 \]

Step 4: Compare P-value with Significance Level

The significance level is $ \alpha = 0.01 $. Since the P-value $ 0.0035 < 0.01 $, we reject the null hypothesis $ H_0 $.

Step 5: Conclusion

There is sufficient evidence to support the claim that less than $ 10\% $ of all subscribers would continue subscribing if fees were raised by $ 20\% $.

Final Answer

$\boxed{\text{Reject } H_0}$

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