Math  /  Data & Statistics

QuestionLet xx be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the xx distribution is μ=7,4+A\mu=7,4+A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 31 patients with arthritis took the drug for 3 months. Blood tests showed that xˉ=8.6\bar{x}=8.6 with sample standard deviation s=3.1s=3.1. Use a 5%5 \% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood. Ω\Omega USE SALT (a) What is the level of significance? \square State the null and alternate hypotheses. (Enter !=!= for \neq as needed.) H0\mathrm{H}_{0} : \square H1H_{1} : \square (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. We'll use the Student's tt, since the sample size is large and σ\sigma is unknown. We'll use the standard normal, since the sample size is large and σ\sigma is unknown. We'll use the standard normal, since the sample size is large and σ\sigma is known. We'll use the Student's tt, since the sample size is large and σ\sigma is known.
Compute the appropriate sampling distribution value of the sample test statistic. (Round your answer to two decimal places.) \square

Studdy Solution
Make a decision based on the test statistic and level of significance:
Since this is a two-tailed test at the 5%5\% significance level, we compare the calculated tt-value to the critical tt-values from the tt-distribution table for 3030 degrees of freedom (n1n-1).
If t>tα/2|t| > t_{\alpha/2}, we reject the null hypothesis.
The computed test statistic is:
2.15 \boxed{2.15}

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