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3 years ago

What number r missing 77,73,69,65

Mathematics

2 answers:

Ad libitum [116K]3 years ago

8 0

81,85,89 are the missing numbers

Gnesinka [82]3 years ago

5 0

Answer:

Step-by-step explanation:

All the numbers are odd and have a difference of two between the next term.

Therefore, the answer can be found by adding 2 to 65 or subtracting two from 69.

Hopefully this helps!

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A sample of 42 observations is selected from one population with a population standard deviation of 3.3. The sample mean is 101.

IrinaVladis [17]

Answer:

$|z| < 2.054$ : Do not reject the null hypothesis.

$|z| > 2.054$ : Reject the null hypothesis.

b) $z = 2.81$

c) Reject.

d) The p-value is 0.005.

Step-by-step explanation:

Before testing the hypothesis, we need to understand the central limit theorem and the subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Population 1:

Sample of 42, standard deviation of 3.3, mean of 101, so:

$\mu_1 = 101$

$s_1 = \frac{3.3}{\sqrt{42}} = 0.51$

Population 2:

Sample of 53, standard deviation of 3.6, mean of 99, so:

$\mu_2 = 99$

$s_2 = \frac{3.6}{\sqrt{53}} = 0.495$

H0 : μ1 = μ2

Can also be written as:

$H_0: \mu_1 - \mu_2 = 0$

H1 : μ1 ≠ μ2

Can also be written as:

$H_1: \mu_1 - \mu_2 \neq 0$

The test statistic is:

$z = \frac{X - \mu}{s}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, and s is the standard error .

a. State the decision rule.

0.04 significance level.

Two-tailed test(test if the means are different), so between the 0 + (4/2) = 2nd and the 100 - (4/2) = 98th percentile of the z-distribution, and looking at the z-table, we get that:

$|z| < 2.054$ : Do not reject the null hypothesis.

$|z| > 2.054$ : Reject the null hypothesis.

b. Compute the value of the test statistic.

0 is tested at the null hypothesis:

This means that $\mu = 0$