An agency reported that in a recent year 43.8% of businesses that employed 200 persons or more received orders via the Internet. Assume a more recent survey has been carried out in 3206 businesses that employ 200 or more persons. Results show that 1488  of them have received orders via the Internet during the past 12 months.
At the 0.10 level of​ significance, use a hypothesis test to try to prove that the percentage of large businesses that receive orders via the Internet has increased from 43.8%
Let π be the hypothesised proportion of successes in the population. State the null​ hypothesis, H0, and the alternative​ hypothesis, H1.

To conduct a hypothesis test for the given problem, we'll follow these steps:

### Step 1: Define the Hypotheses
We are testing if the percentage of businesses that receive orders via the Internet has increased from the previous 43.8%. Therefore, the hypotheses are:

- **Null Hypothesis (H₀):** The percentage has **not increased**, meaning it is still 43.8%.  
  \[
  H_0: \pi = 0.438
  \]

- **Alternative Hypothesis (H₁):** The percentage **has increased**.  
  \[
  H_1: \pi > 0.438
  \]
This is a **right-tailed test**, as we are interested in whether the proportion has increased.

### Step 2: State the significance level
The significance level given is \(\alpha = 0.10\).

Next steps involve calculating the test statistic using the sample proportion (\(p\)) and the hypothesized proportion (\(\pi_0 = 0.438\)).

Would you like me to continue with the calculation, or do you have any specific questions so far?

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Here are 5 related questions:

1. How do you calculate the sample proportion \(p\) from the data provided?
2. What is the formula for the test statistic \(z\) in a proportion hypothesis test?
3. How do you find the critical value for a right-tailed test at a 0.10 significance level?
4. What are Type I and Type II errors in hypothesis testing?
5. How would you interpret a p-value in the context of this hypothesis test?

**Tip**: Always ensure to clearly state your null and alternative hypotheses before starting a hypothesis test.

An agency reported that in a recent year 43.8% of businesses that employed 200 persons or more received orders via the Internet. Assume a more recent survey has been carried out in 3206 businesses that employ 200 or more persons. Results show that 1488 of them have received orders via the Internet during the past 12 months. At the 0.10 level of significance, use a hypothesis test to try to prove that the percentage of large businesses that receive orders via the Internet has increased from 43.8%. Let π be the hypothesized proportion of successes in the population. State the null hypothesis, H0, and the alternative hypothesis, H1.

Conduct a hypothesis test to determine if the percentage of large businesses receiving Internet orders has increased from 43.8%. Learn to define null and alternative hypotheses, calculate the sample proportion, and apply the Z-test at a 0.10 significance level. Suitable for college-level statistics.

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