Question

A group of graduate students conducting a research program related to human health. They wanted to test the claim that average life span of residents of their state is less than 75 years. They have collected the following random sample of 27 ages (in years) from recent obituary notices. They have learned further that the life span distribution in this state is normally distributed. 77 68 83 93 58 33 78 94 83 84 77 70 85 97 78 71 86 66 66 29 69 82 90 43 50 81 88 Does this information indicate that the population mean life span of residents is less than 75 years? Use a 0.05 level of significance. a) What is the sample mean life span? b) What is sample standard deviation of life span? c) State the null and alternative hypotheses. d) What is the degrees of freedom of the t distribution? e) What is the value of the test statistic? Give four decimal places f) What is the p-value? Give four decimal places g) What is your conclusion? Write in terms of whether you have evidence to support the claim.

          A group of graduate students conducting a research program related to human health. They wanted to test the claim that average life span of residents of their state is less than 75 years. They have collected the following random sample of 27 ages (in years) from recent obituary notices. They have learned further that the life span distribution in this state is normally distributed.
77  68  83  93  58  33  78  94  83  84 77  70  85  97  78  71  86  66  66  29  69  82  90  43  50  81  88 

Does this information indicate that the population mean life span of residents is less than 75 years? Use a 0.05 level of significance.

a) What is the sample mean life span?

b) What is sample standard deviation of life span?

c) State the null and alternative hypotheses.

d) What is the degrees of freedom of the t distribution?

e) What is the value of the test statistic? Give four decimal places

f) What is the p-value? Give four decimal places

g) What is your conclusion? Write in terms of whether you have evidence to support the claim.

Show more…

Added by Curtis K.

Understandable Statistics Concepts and Methods

Charles Brase, Corrinne Brase 12th Edition

Chapter 8

Instant Answer

Solved by Expert Jon Southam

06/30/2022

Step 1

Given data: 77, 68, 83, 93, 58, 33, 78, 94, 83, 84, 77, 70, 85, 97, 78, 71, 86, 66, 66, 29, 69, 82, 90, 43, 50, 81, 88 Add all the ages and divide by the number of ages (27): \[ \text{Sample Mean} = \frac{77 + 68 + 83 + \ldots + 81 + 88}{27} = 73.2963 \] ** Show more…

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A group of graduate students conducting a research program related to human health. They wanted to test the claim that average life span of residents of their state is less than 75 years. They have collected the following random sample of 27 ages (in years) from recent obituary notices. They have learned further that the life span distribution in this state is normally distributed. 77 68 83 93 58 33 78 94 83 84 77 70 85 97 78 71 86 66 66 29 69 82 90 43 50 81 88 Does this information indicate that the population mean life span of residents is less than 75 years? Use a 0.05 level of significance. a) What is the sample mean life span? b) What is sample standard deviation of life span? c) State the null and alternative hypotheses. d) What is the degrees of freedom of the t distribution? e) What is the value of the test statistic? Give four decimal places f) What is the p-value? Give four decimal places g) What is your conclusion? Write in terms of whether you have evidence to support the claim.

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Transcript

00:01 All right, so we're looking at the average age of lifespan of residence in their state.

00:10 And they want to see, is it less than 75 years old? so they collected a random sample of 27 ages from recent obadiary notices, and they noticed they noted the ages.

00:22 And we're going to see if this information indicates that the population being lifespan of residence is less than 75 years.

00:30 And we're testing at the alpha 0 .05.

00:34 So what is the sample mean lifespan? so we take all the values to add them up, divide by 27.

00:40 We get this number.

00:41 So 73 .2.

00:46 0 .3 years.

00:49 Sample standard deviation is 17 .68 years.

00:54 We'll round to 7.

00:57 State the null and alternative hypotheses.

01:00 So the null hypothesis is that the mean age is equal to 75.

01:07 You might even see greater than equal to 75.

01:13 But the alternative hypothesis is that the mean is less than 75, strictly less than 75.

01:22 The degrees of freedom of the t distribution, well degrees of freedom are given as n minus 1.

01:28 In this case, n is 27, so we get 26.

01:32 The value of the test statistic.

01:36 So this is part e here.

01:38 That's given as it's going to be x bar minus mu over sample standardvation for root n.

01:45 This s over root n, that's sometimes called, or that is called the standard error of the mean.

01:52 And when you have a sample, you address that.

01:57 That's a way to ensure you're capturing the true distribution, or the true mean...

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