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3 years ago

Use the following information to complete parts I, II and III.

Mathematics

1 answer:

Ber [7]3 years ago

7 0

Answer:

see below

Step-by-step explanation:

Part I: Use scientific notation to estimate the number of hours in one year

Using the conversion factors

Estimate using scientific notation

31,556,952 seconds = 3.2 * 10^7

3600 seconds = 3.6 * 10 ^2

1 year = 3.2 * 10^7 seconds * 1 hour/ 3.6 * 10 ^2 seconds

3.2 /3.6 =.88888 (repeating)

10^7 / 10^2 = 10^5

8.88888 * 10 ^5

8.888 * 10 ^4 hours

Part II: Use scientific notation to calculate the exact number of hours in one year.

31,556,952 seconds = 3.1556952 * 10^7

3600 seconds = 3.6 * 10 ^2

1 year = 3.1556952 * 10^7 seconds * 1 hour/ 3.6 * 10 ^2 seconds

3.1556952 /3.6 =.876582

10^7 / 10^2 = 10^5

.876582 * 10 ^5

8.76582*10^4 hours

Part III: In two or more complete sentences, compare your answers to parts I and II. In your comparison, discuss similarities and differences in your answers.

Part II is an exact answer, where Part I is an estimate. Both Parts give values in the thousands of hours, and are both between 8700 and 8900 hours. Part I can be done without a calculator where Part II is much harder to do without a calculator.

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guajiro [1.7K]

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The null hypothesis is $H_o : \sigma^2_1 = \sigma^2 _2$

The alternative hypothesis is $H_a : \sigma_1 ^2 > \sigma^2_2$

$F_{critical} = 1.8608$

$F = 2.9085$

The decision rule is

Reject the null hypothesis

There is sufficient evidence to support the researchers claim

Step-by-step explanation:

From the question we are told that

The first sample size is $n_1 = 30$

The sample variance for elementary school is $s^2_1 = 8324$

The second sample size is $n_2 = 30$

The sample variance for the secondary school is $s^2_2 = 2862$

The significance level is $\alpha = 0.05$

The null hypothesis is $H_o : \sigma^2_1 = \sigma^2 _2$

The alternative hypothesis is $H_a : \sigma_1 ^2 > \sigma^2_2$

Generally from the F statistics table the critical value of $\alpha = 0.05$ at first and second degree of freedom $df_1 = n_1 - 1 = 30 - 1 = 29$ and $df_2 = n_2 - 1 = 30 - 1 = 29$ is