Question

systolic blood pressure levels above 120 mm hg are considered to be high. for the 100 systolic blood pressure levels listed in the accompanying data set, the mean is 120.74000 mm hg and the standard deviation is 14.70098 mm hg. assume that a simple random sample has been selected. use a 0.10 significance level to test the claim that the sample is from a population with a mean greater than 120 mm hg. click the icon to view the data set of systolic blood pressure levels. identify the null and alternative hypotheses. ( h_0: mu = 120 ) ( h_1: mu > 120 ) (type integers or decimals. do not round.) identify the test statistic. 0.50 (round to two decimal places as needed.) identify the p - value. (round to three decimal places as needed.)

Explanation:

Step1: <Find the P - value for a one - tailed z - test>

The test statistic \(z = 0.50\). For a right - tailed (since \(H_1:\mu>120\)) z - test, the P - value is \(P(Z>z)\). Using the standard normal distribution, \(P(Z > 0.50)=1 - P(Z\leq0.50)\).
From the standard normal table, \(P(Z\leq0.50)=0.6915\).

Step2: <Calculate the P - value>

\(P(Z>0.50)=1 - 0.6915 = 0.3085\approx0.309\)

Answer:

\(0.309\)