Lin drew a triangle and a dilation of the triangle with scale factor 2

Step-by-step explanation:

Lin drew a triangle and a dilated triangle with a scale factor of .

That means image of the original triangle is smaller than the preimage.

1). Center of dilation will be point A.

   Since, triangle ACB has been reduced to form triangle ADE by a scale factor of

Scale factor = =

AD =

So the center of dilation is point A.

2). Since triangle ADE is half of the triangle ACB, triangle ACB is preimage (original) and triangle ADE is an image after dilation.

We conclude that the younger group have a lower mean time in seconds than the older group.

Step-by-step explanation:

We are given that for 24 younger adults (21-36 years), the average time for navigation entry was 31.4 seconds versus 40 seconds for the 24 participants in the older group (55-75 years).

Standard deviations are not given, so we estimate the younger group at 0.99 seconds and the older group at 1.04 seconds.

We have to conduct a hypothesis test to see whether the younger group have a lower mean time in seconds than the older group.

Let = population mean time for navigation entry for younger groups

      = population mean time for navigation entry for older groups

SO, Null Hypothesis, :    or    {means that the younger group have a mean time in seconds higher than or equal to the older group}

Alternate Hypothesis, :  or    {means that the younger group have a lower mean time in seconds than the older group}

The test statistics that will be used here is Two-sample t test statistics as we don't know about the population standard deviations;

               T.S. =  ~  

where, = sample average time for navigation entry for younger adults (21-36 years) = 31.4 seconds

= sample average time for navigation entry for older adults (55-75 years) = 40 seconds

  = standard deviation for 24 younger adults = 0.99 seconds

  = standard deviation for 24 participants in the older group = 1.04 seconds

 = sample size of younger adults = 24

  = sample size of older adults = 24

Here, = = 1.015

So, test statistics =    ~

                               = -29.35

So, at 0.05 level of significance, the t table gives critical value of -1.6792 at 46 degree of freedom for one-tailed test. Since our test statistics is way less than the critical value of t so we have sufficient evidence to reject null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the younger group have a lower mean time in seconds than the older group.