//he Student\'s t distribution table gives critical values for the Student\'s t

Question

//he Student's t distribution table gives critical values for the Student's t distribution. Use an appropriate d.f. as the row header. For a right-tailed test, the column header is the value of found in the one-tail area row. For a left-tailed test, the column header is the value of found in the one-tail area row, but you must change the sign of the critical value t to t. For a two-tailed test, the column header is the value of from the two-tail area row. The critical values are the ±t values shown.

Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is = 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 36 patients with arthritis took the drug for 3 months. Blood tests showed that

x = 8.0 with sample standard deviation s = 1.7. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood. Solve the problem using the critical region method of testing (i.e., traditional method). (Round your answers to three decimal places.)

Find the

critical value = ±

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: = 7.4

Alternative hypothesis: 7.4

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample mean is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 0.2833

DF = n - 1 = 36 - 1

D.F = 35

t = (x - ) / SE

t = 2.12

tcritical = + 2.030

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

Since we have a two-tailed test, the critical region is

- 2.030 > t > 2.030

Interpret results. Since the t-value (2.12) lies in the critical region, we have to reject the null hypothesis.

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