Questions: In 2022, the average time spent online by people in the Philippines was estimated to be 10.45 hours. Researchers want to test if these values were lower in 2023. Choose the correct null and alternative hypothesis. H0: μ=10.45 HA: μ<10.45

In 2022, the average time spent online by people in the Philippines was estimated to be 10.45 hours. Researchers want to test if these values were lower in 2023.

Choose the correct null and alternative hypothesis.
H0: μ=10.45
HA: μ<10.45

Transcript text: In 2022, the average time spent online by people in the Philippines was estimated to be 10.45 hours. Researchers want to test if these values were lower in 2023. Choose the correct null and alternative hypothesis. $H_{0}: \mu=10.45$ $H_{A}: \mu<10.45$

Solution

Solution Steps

Step 1: Define Hypotheses

We are testing whether the average time spent online by people in the Philippines in 2023 is lower than the average of 10.45 hours from 2022. The hypotheses are defined as follows:

Null Hypothesis ($H_0$): $ \mu = 10.45 $
Alternative Hypothesis ($H_A$): $ \mu < 10.45 $

Step 2: Calculate Standard Error

The standard error ($SE$) is calculated using the formula:

\[ SE = \frac{\sigma}{\sqrt{n}} = \frac{1.5}{\sqrt{100}} = 0.15 \]

Step 3: Calculate Test Statistic

The test statistic ($Z_{test}$) is calculated using the formula:

\[ Z_{test} = \frac{\bar{x} - \mu_0}{SE} = \frac{10.2 - 10.45}{0.15} = -1.6667 \]

Step 4: Calculate P-value

For a left-tailed test, the p-value is determined as follows:

\[ P = T(z) = 0.0478 \]

Step 5: Conclusion

To determine whether to reject the null hypothesis, we compare the p-value to the significance level ($\alpha = 0.05$). Since $0.0478 < 0.05$, we reject the null hypothesis.

Final Answer

The results indicate that there is sufficient evidence to conclude that the average time spent online by people in the Philippines in 2023 is lower than 10.45 hours.

$\boxed{H_A: \mu < 10.45}$

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