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A study is done to determine if students in the California state university system (sample 1) take longer to graduate, on averag

Debora [2.8K]

Answer:

We conclude that the students in the California state university system take longer to graduate as compared to students enrolled in private universities.

Step-by-step explanation:

We are given that from years of research, it is known that the population standard deviations are 1.5 years and 0.9 years, respectively.

One hundred students from each the California state university system and private universities are surveyed. The California state university system students took on average 4.8 years while the private university students took on average 4.4 years.

Let $\mu_1$ = population average time taken by students in the California state university system to graduate

$\mu_2$ = population average time taken by students in the private universities to graduate

SO, Null Hypothesis, $H_0$ : $\mu_1-\mu_2\leq0$ or $\mu_1 \leq \mu_2$ {means that the students in the California state university system take less than or equal time to graduate as compared to students enrolled in private universities}

Alternate Hypothesis, $H_A$ : $\mu_1-\mu_2 >0$ or $\mu_1>\mu_2$ {means that the students in the California state university system take longer to graduate as compared to students enrolled in private universities}

The test statistics that will be used here is Two-sample z test statistics as we know about the population standard deviations;

T.S. = $\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{\sqrt{\frac{\sigma_1^{2} }{n_1} + \frac{\sigma_2^{2} }{n_2}} }$ ~ N(0,1)

where, $\bar X_1$ = sample average time taken by the California state university system students to graduate = 4.8 years

$\bar X_2$ = sample average time taken by the private university students to graduate = 4.4 years

$\sigma_1$ = population standard deviation for California state university system students = 1.5 years

$\sigma_2$ = population standard deviation for private university students = 0.9 years

$n_1$ = sample of California state university system students taken = 100

$n_2$ = sample of private university students taken = 100

So, test statistics = $\frac{(4.8-4.4)-(0)}{\sqrt{\frac{1.5^{2} }{100} + \frac{0.9^{2} }{100}} }$

= 2.287

Now at 0.10 significance level, the z table gives critical value of 1.2816 for right-tailed test. Since our test statistics is more than the critical value of z so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the students in the California state university system take longer to graduate as compared to students enrolled in private universities.

5 0

4 years ago

HELP ASAP WITH THIS QUESTION

alexgriva [62]

Hey there (again)

$x = 2y \\ y = -2 \\ x = 2(-2) \\x= -4 \\ \\ \\ w + xy + 4x^2 = 2\\ w+-4(-2) + 3(-4)^2 = 2 \\ w + 8 + 3(16) = 2 \\ w + 8 + 48 = 2 \\ Subtract56: w + 56 =2 \\ 56 - 56 (Cancel) \\ 2 - 56 = -54 \\ w = -54$

Answer: $B$ the simplification performed in step 2 is invalid or incorrect

Good luck on your assignment and enjoy your day

~ $MeIsKaitlyn:)$

5 0

4 years ago

HELP HELP PLEASE!! D: Determine the missing side length: Please don't give cap!

viktelen [127]

Answer:

c = 35

Step-by-step explanation:

$c^{2} = a^{2} + b^{2}$

$c^{2} = 21^{2} + 28^{2}$

$c^{2} = 1225$

$\sqrt{c^{2} } = \sqrt{1225}$

$c = 35$

8 0

3 years ago

Bethany wants to estimate the value of (4.296 times 10 Superscript 11) (1.8614 times 10 Superscript negative 14). Which statemen

avanturin [10]

Answer:

D. The number will be less than 1 because when adding the exponents,

11 + (-14) = -3, and a number in scientific notation with a negative exponent is less than 1.

Step-by-step explanation:

The question lacks appropriate option. Find the options below;

A. The value will be greater than 1 because 4.296 x 10^11 is a very large number and multiplication always increases the size of a number.

B. The value will be greater than 1 because 4 x 2 = 8 and 8 is larger than 1.

C. The value will be less than 1 because (4.296 x 10^11) x (1.8614 x 10^-14) will be a negative number. All negative numbers are less than one.

D. The number will be less than 1 because when adding the exponents,

11 + (-14) = 3, and a number in scientific notation with a negative exponent is less than 1.

Given the expression $(4.296*10^{11})(1.8614*10^{-14})$ , to expand the expression we will apply some of the law of indices below. If a, b and m are integers

$a^m*a^n = a^{a+m}$

$= (4.296*10^{11})(1.8614*10^{-14})\\\\= (4.296*1.8614)(10^{11}*10^{-14}) \\\\= 7.9965744 * 10^{11}*10^{-14}\\sum \ up \ the\ power\ of\ the \ exponents\\\\= 7.9965744 *10^{11-14}\\\\= 7.9965744 *10^{-3}\\$

= 0.0079965744

Based on the result, it can be seen that the resulting value is less than 1 due to the negative power of its exponent (i.e -3). Any scientific notation having a negative exponent always returns a value that is less than 1.

4 0

3 years ago

Read 2 more answers

-9 is an example of what

lyudmila [28]

Answer:

A negative number, a negative integer, a negative multiple of 3, etc.

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers