Question

QUESTION 3 "In interval estimation, as the sample size becomes larger, the interval estimate" becomes narrower. becomes wider. "remains the same, because the mean is not changing." gets closer to 1.96. ОО QUESTION 4 "A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal. Using a - .05, it can be concluded that the population mean age is" not significantly different from 24. significantly different from 24. significantly less than 24. significantly more than 24.

Answer 1

Solution :

3) The interval estimate is given as follows :

Interval estimate : (Point estimate ± Margin of error)

As the sample size increases the margin of error gets smaller, which results in the narrower Interval estimate.

Hence,

In interval estimation, as the sample size becomes larger, the interval estimate becomes narrower.

First option is correct.

4) Null and alternative hypotheses :

HO :μ 24

$\large H_{1}: \mu > 24$

Test statistic :

To test the hypothesis the most appropriate test is one sample t-test. The test statistic is given as follows :

$\large t = \frac{\bar{x}-\mu}{s/\sqrt{n}}$

Where, x̄ is sample mean, s is sample standard deviation, n is sample size and μ is hypothesized value of population mean under H_{​​​​​​0}.

We are given the following values :

$\large \bar{x} = 25,\ \mu = 24,\ s = 2,\ n = 16$

$\large \therefore t = \frac{(25-24)}{(2/\sqrt{16})} = 2$

The value of the test statistic is 2.

P-value :

Since, our test is right-tailed test, therefore we shall obtain right-tailed p-value for the test statistic. The right-tailed p-value is given as follows :

P-value = P(T > t)

P-value = P(T > 2)

P-value = 0.0320

The p-value is 0.0320.

Decision :

Significance level = 0.05

P-value = 0.0320

(0.0320 < 0.05)

Since, p-value is less than the significance level of 0.05, therefore we shall reject the null hypothesis at 0.05 significance level.

Conclusion :

At 0.05 significance level, there is sufficient evidence to conclude that average age of all the students at the university is significantly more than 24.

Last option is correct.

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