What does the null hypothesis state in hypothesis testing?
No significant difference
The alternative hypothesis contradicts the null hypothesis.
What type of error is committed when rejecting a true null hypothesis?
Type I error
Common values for the significance level include 0.05, 0.01, and 0.10
Lower significance levels are used when falsely rejecting the null hypothesis has serious repercussions.
Match the significance level with its Type I error probability:
0.05 (5%) ↔️ 5%
0.01 (1%) ↔️ 1%
0.10 (10%) ↔️ 10%
What is the definition of a Type I error in hypothesis testing?
Rejecting a true null hypothesis
The choice of significance level depends on the consequences of a Type I error
What is the formula for calculating the test statistic in a normal distribution hypothesis test?
z = \frac{\bar{x} - μ}{\frac{σ}{\sqrt{n}}}</latex>
In the test statistic formula, σ represents the population standard deviation.
What is the first step in determining the critical region in hypothesis testing?
Identify the significance level
The critical region is the set of values for the test statistic that lead to rejecting the null hypothesis
In hypothesis testing, μ represents the population mean stated in the null hypothesis.
σ is the sample standard deviation.
False
In an example, we have a sample of 36 apples with a mean weight of 105g</latex>. The null hypothesis states that the population mean weight is 100g. The population standard deviation is 10g. Using the formula, the calculated z-value is approximately 3.00.
Steps to determine the critical region in hypothesis testing
1️⃣ Identify the significance level (α).
2️⃣ Determine if the test is one-tailed or two-tailed.
3️⃣ Use standard normal distribution tables to find the critical value(s) corresponding to (α).
Match the significance level with its critical value for a one-tailed test:
0.05 ↔️ 1.645
0.01 ↔️ 2.33
0.10 ↔️ 1.28
The null hypothesis states that there is a significant difference or effect.
False
A Type I error occurs when we reject a true null hypothesis.
What is the formula for calculating the test statistic in a normal distribution?
z = \frac{\bar{x} - μ}{\frac{σ}{\sqrt{n}}}</latex>
If the calculated z-value is 3.00, it is greater than the critical value for a one-tailed test with α=0.05.
For a one-tailed test with α=0.05, the critical value is 1.645.
In hypothesis testing, we can reject the null hypothesis if the test statistic falls within the critical region.
What should you use to find critical values for hypothesis testing?
Standard normal distribution tables
The critical value for a one-tailed test with α=0.05 is 1.645
The critical value for a two-tailed test with α=0.01 is ±2.58.
What is the critical value for a one-tailed test with α=0.10?
1.28
Steps to make a decision in hypothesis testing
1️⃣ Compare the test statistic to the critical value
2️⃣ Compare the p-value to α
3️⃣ Reject H0 if the test statistic is more extreme or the p-value is less than α
4️⃣ Fail to reject H0 otherwise
What should you do if the test statistic is more extreme than the critical value?
Reject H0
If the p-value is greater than α, you should reject H0.
False
For a p-value less than α, you should reject H0.
What does it mean if you reject H0?
Significant evidence supports H1
If you fail to reject H0, it means there is enough evidence to support H1.