Question

Your company markets a computerized device for detecting high blood pressure. The device measures an individual’s blood pressure once per hour at a randomly selected time throughout a 12-hour period. Then it calculates the mean systolic (top number) pressure for the sample of measurements. Based on the sample results, the device determines whether there is significant evidence that the individual’s actual mean systolic pressure is greater than 130. If so, it recommends that the person seek medical attention.

(a) State appropriate null and alternative hypotheses in this setting. Be sure to define your parameter.

(b) Describe a Type I and a Type II error, and explain the consequences of each.

(c) The blood pressure device can be adjusted to decrease one error probability at the cost of an increase in the other error probability. Which error probability would you choose to make smaller, and why?

Short answer

a. $H_0:\mu =130$- null hypothesis and $H_a:\mu >130$- alternate hypothesis

b. Type I error - systolic pressure = $130$but tests show it is more. Type II error- systolic pressure is more than $130$but tests show it is equal

c. Type II error

Step-by-step solution

introduction

The null hypothesis is an overall explanation that expresses that there is no correlation between two peculiarities viable or that there is no association between two gatherings. An alternative hypothesis is an explanation that describes that there is a relation between two chosen variables in a study

explanation part (a)

Mean systolic blood pressure is $130$

Now,

$H_0:\mu =130$as per the null hypothesis

$H_a:\mu >130$as per the alternative hypothesis

Thus, systolic pressure = $130$for null hypothesis and more than$130$for alternative hypothesis.

explanation part (b)

Type I error- Null hypothesis is correct and it is dimissed. The mean systolic pressure is equivalent to $130$yet the test indicates that the mean systolic tension is more. Thus, the outcome is that they have high circulatory strain and made a move against a high pulse however in reality they don't have a high pulse.

In Type Il error- when the null theories are valid then a rejection of $H_0$additionally failed.

The mean systolic strain is more than $130$yet the test indicates that the mean systolic tension is equivalent to $130$. Thus, the result is that they have typical circulatory strain and did not make a move against high pulse however in reality they have high pulse and action ought to be taken.

explanation part (c)

Type II error probability should be smaller as the person can die since there is no treatment for high blood pressure.