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Usimov [2.4K]
2 years ago
7

In two or more complete sentences write and solve an equation for the situation and explain how you will solve the equation. Aft

er an 8-week exercise program Grace lost 45 pounds. She now weighs 122 pounds. How much did Grace weigh before she started her exercise program?
Mathematics
1 answer:
notka56 [123]2 years ago
7 0

Answer:

Grace weighed 167 pounds before she started her exercise program.

Step-by-step explanation:

Given,

Weight lost by Grace = 45 pounds

Weight of Grace after exercise weeks = 122 pounds

Let,

x represents the weight of Grace before she started the exercise program.

Loss means subtraction, therefore,

We will subtract the lost weight from original weight.

Original weight - Weight lost = Weight after exercise weeks

x - 45 = 122

Adding 45 on both sides

x - 45+ 45= 122+45

x=167   pounds

Grace weighed 167 pounds before she started her exercise program.

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Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic t.
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Using the t-distribution, it is found that the p-value of the test is 0.007.

At the null hypothesis, it is <u>tested if the mean lifetime is not greater than 220,000 miles</u>, that is:

H_0: \mu \leq 220000

At the alternative hypothesis, it is <u>tested if the mean lifetime is greater than 220,000 miles</u>, that is:

H_1: \mu > 220000.

We have the <u>standard deviation for the sample</u>, thus, the t-distribution is used. The test statistic is given by:

t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}

The parameters are:

  • \overline{x} is the sample mean.
  • \mu is the value tested at the null hypothesis.
  • s is the standard deviation of the sample.
  • n is the sample size.

For this problem:

\overline{x} = 226450, \mu = 220000, s = 11500, n = 23

Then, the value of the test statistic is:

t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}

t = \frac{226450 - 220000}{\frac{11500}{\sqrt{23}}}

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Using a t-distribution calculator, the p-value of the test is of 0.007.

A similar problem is given at brainly.com/question/13873630

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