In a study of parents' perceptions of their children's size, researchers asked parents to estimate their youngest child's height. The researchers hypothesize that parents tend to underestimate their youngest child's size because the youngest child is the baby of the family and all other family members appear larger compared to the baby. The sample of 39 parents who were surveyed underestimated their youngest child's height by 7.5 cm on average; the standard deviation for the difference in actual heights and estimated heights was 7.2 cm, and the data were approximately normal.

Determine the TS and p-value for this study.

Test statistic t=6.505

P-value=0

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that parents tend to underestimate their youngest child's size.

Then, the null and alternative hypothesis are:

The significance level is assumed to be 0.05.

The sample has a size n=39.

The sample mean is M=7.5.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=7.2.

The estimated standard error of the mean is computed using the formula:

Then, we can calculate the t-statistic as:

The degrees of freedom for this sample size are:

This test is a right-tailed test, with 38 degrees of freedom and t=6.505, so the P-value for this test is calculated as (using a t-table):

As the P-value (0) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is  enough evidence to support the claim that parents tend to underestimate their youngest child's size.

the workers who do no drive has no reasonable reason to buy gasoline due to they don't have anything to use it for

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.