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Answer :
Certainly! Let's walk through the solution for this hypothesis testing question step by step.
1. Identify the Null and Alternative Hypotheses:
- The null hypothesis ([tex]\(H_0\)[/tex]) is a statement that there is no effect or no difference, and it often includes the equality sign. In this context, the null hypothesis is:
[tex]\[
H_0: \mu = 5.00 \text{ Mbps}
\][/tex]
- The alternative hypothesis ([tex]\(H_1\)[/tex]) is what you want to test for. It's typically showing a difference or effect. Since the question mentions conducting a hypothesis test with all conditions met, and you should examine a two-tailed test (meaning you're checking for any difference from 5.00 Mbps, not just greater or less), the alternative hypothesis would be:
[tex]\[
H_1: \mu \neq 5.00 \text{ Mbps}
\][/tex]
2. Identify the Test Statistic:
- The test statistic is a value that results from standardizing the sample statistic, which helps us determine how far our sample statistic is from the null hypothesis value, under the assumption that the null hypothesis is true.
- For this problem, the test statistic is provided as:
[tex]\[
-2.30
\][/tex]
- This value is already rounded to two decimal places.
3. Identify the P-value:
- Typically, the P-value is a measure of how much evidence we have against the null hypothesis. In hypothesis testing, it helps us decide whether to reject the null hypothesis.
- To determine the P-value from a test statistic in a two-tailed test, generally, you would find the probability associated with the extreme values of a normal distribution.
- Without the specific computation details or the context of degrees of freedom or sample size here, we can't provide the exact P-value numerically. However, if you have access to statistical tables or a computational tool, you would use it to find the P-value corresponding to your test statistic of [tex]\(-2.30\)[/tex].
In conclusion, the null hypothesis is [tex]\(H_0: \mu = 5.00 \text{ Mbps}\)[/tex], the alternative hypothesis is [tex]\(H_1: \mu \neq 5.00 \text{ Mbps}\)[/tex], and the test statistic is [tex]\(-2.30\)[/tex].
1. Identify the Null and Alternative Hypotheses:
- The null hypothesis ([tex]\(H_0\)[/tex]) is a statement that there is no effect or no difference, and it often includes the equality sign. In this context, the null hypothesis is:
[tex]\[
H_0: \mu = 5.00 \text{ Mbps}
\][/tex]
- The alternative hypothesis ([tex]\(H_1\)[/tex]) is what you want to test for. It's typically showing a difference or effect. Since the question mentions conducting a hypothesis test with all conditions met, and you should examine a two-tailed test (meaning you're checking for any difference from 5.00 Mbps, not just greater or less), the alternative hypothesis would be:
[tex]\[
H_1: \mu \neq 5.00 \text{ Mbps}
\][/tex]
2. Identify the Test Statistic:
- The test statistic is a value that results from standardizing the sample statistic, which helps us determine how far our sample statistic is from the null hypothesis value, under the assumption that the null hypothesis is true.
- For this problem, the test statistic is provided as:
[tex]\[
-2.30
\][/tex]
- This value is already rounded to two decimal places.
3. Identify the P-value:
- Typically, the P-value is a measure of how much evidence we have against the null hypothesis. In hypothesis testing, it helps us decide whether to reject the null hypothesis.
- To determine the P-value from a test statistic in a two-tailed test, generally, you would find the probability associated with the extreme values of a normal distribution.
- Without the specific computation details or the context of degrees of freedom or sample size here, we can't provide the exact P-value numerically. However, if you have access to statistical tables or a computational tool, you would use it to find the P-value corresponding to your test statistic of [tex]\(-2.30\)[/tex].
In conclusion, the null hypothesis is [tex]\(H_0: \mu = 5.00 \text{ Mbps}\)[/tex], the alternative hypothesis is [tex]\(H_1: \mu \neq 5.00 \text{ Mbps}\)[/tex], and the test statistic is [tex]\(-2.30\)[/tex].
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