Hypothesis Testing Math Example 2

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Example 2

hard
A medication is claimed to reduce blood pressure by 10 mmHg on average. A clinical trial with n=49n=49 patients shows xห‰=8.2\bar{x}=8.2 mmHg reduction, s=7s=7 mmHg. Test H0:ฮผ=10H_0: \mu=10 vs Ha:ฮผโ‰ 10H_a: \mu \neq 10 at ฮฑ=0.05\alpha=0.05.

Solution

  1. 1
    Test statistic: z=8.2โˆ’107/49=โˆ’1.81=โˆ’1.8z = \frac{8.2 - 10}{7/\sqrt{49}} = \frac{-1.8}{1} = -1.8
  2. 2
    Two-tailed p-value: p=2ร—P(Z<โˆ’1.8)=2ร—0.0359=0.0718p = 2 \times P(Z < -1.8) = 2 \times 0.0359 = 0.0718
  3. 3
    Compare: p=0.0718>ฮฑ=0.05p = 0.0718 > \alpha = 0.05
  4. 4
    Decision: Fail to reject H0H_0. The observed reduction of 8.2 mmHg is not significantly different from the claimed 10 mmHg at 5% significance level.

Answer

z=โˆ’1.8z=-1.8, p=0.072>0.05p=0.072 > 0.05. Fail to reject H0H_0. Data is consistent with 10 mmHg claim.
Two-tailed tests check whether the parameter differs from the null in either direction, so p-value is doubled. Even though the sample average (8.2) differs from 10, the difference isn't large enough relative to sampling variability to reject the null hypothesis.

About Hypothesis Testing

A systematic method to decide whether sample data provides enough evidence to reject a claim (null hypothesis) about a population parameter.

Learn more about Hypothesis Testing โ†’

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