It is known that a particular laboratory task takes the average person 2.5 seconds. A researcher was interested in whether older people are slower (take longer) on this task. The researcher tested 30 randomly selected 80-year-olds. Their meantime was 2.7 seconds, with an estimated population standard deviation of 1.4 seconds. What should the researcher conclude (use the .05 level)?

 The decision rule is  

Fail to reject the null hypothesis

  The conclusion is

 There is no sufficient evidence to conclude that older people are slower

Step-by-step explanation:

From the question we are told that  

    The average time taken is  

      The  sample size is  

     The sample mean is  

      The standard deviation is  

The null hypothesis is  

The alternative hypothesis  is  

Generally the test statistics is mathematically represented as

=>              

=>              

From the z table  the area under the normal curve to the right corresponding to  0.7825   is  

So from the question we see that the hence

 The decision rule is  

Fail to reject the null hypothesis

  The conclusion is

 There is no sufficient evidence to conclude that older people are slower

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation:

1. perpendicular

2. parallel

3. perpendicular