A t-test is conducted for the null hypothesis H0:μ=10versus the alternative Ha:μ>10for a random sample of n = 17 observations. The test results are t = 1.174, p-value = 0.1288.

a. Interpret the p-value.

Short Answer

Expert verified

a. There is a 12.88% chance that we would observe a test statistic resulting in 1.174.

Step by step solution

01

Given Information

The random sample of size, n=17.

The t-test is conducted for the null and alternative hypothesis H0:μ=10versus Ha:μ>10.

The p-value of the t-test=0.1288.

The test statistic calculated is, t=1.174.

02

Stating the statistical hypothesis t-test.

The t-test statistic is a sample statistic, computed from information provided in the sample that the researchers use to decide between the null and alternative hypotheses.

03

Interpreting the p-value result.

a. The p-value is a value used to validate the hypothesis against observed data. So, at which we should obtain a value at least as extreme as the observed result, assuming the truth of the null hypothesis. Thus, in our case is a 12.88% chance that we would observe a test statistic resulting in 1.174.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A random sample of 175 measurements possessed a mean x¯=8.2 and a standard deviation s = .79.

a. Test H0:μ=8.3 against Ha:μ8.3Use a=0.05

: A random sample of n = 200 observations from a binomial population yield

p^=0.29

a. Test H0:p=0.35 against H0:p<0.35. Usea=0.05.

Trading skills of institutional investors. Refer to The Journal of Finance (April 2011) analysis of trading skills of institutional investors, Exercise 7.36 (p. 410). Recall that the study focused on “round-trip” trades, i.e., trades in which the same stock was both bought and sold in the same quarter. In a random sample of 200 round-trip trades made by institutional investors, the sample standard deviation of the rates of return was 8.82%. One property of a consistent performance of institutional investors is a small variance in the rates of return of round-trip trades, say, a standard deviation of less than 10%.

a. Specify the null and alternative hypotheses for determining whether the population of institutional investors performs consistently.

b. Find the rejection region for the test usingα=.05

c. Interpret the value of in the words of the problem.

d. A Minitab printout of the analysis is shown (next column). Locate the test statistic andp-value on the printout.

e. Give the appropriate conclusion in the words of the problem.

f. What assumptions about the data are required for the inference to be valid?


Trading skills of institutional investors. The trading skills of institutional stock investors were quantified and analyzed in The Journal of Finance (April 2011). The study focused on “round-trip” trades, i.e., trades in which the same stock was both bought and sold in the same quarter. Consider a random sample of 200 round-trip trades made by institutional investors. Suppose the sample mean rate of return is 2.95% and the sample standard deviation is 8.82%. If the true mean rate of return of round-trip trades is positive, then the population of institutional investors is considered to have performed successfully.

a. Specify the null and alternative hypotheses for determining whether the population of institutional investors performed successfully.

b. Find the rejection region for the test using\(\alpha = 0.05\).

c. Interpret the value of\(\alpha \)in the words of the problem.

d. A Minitab printout of the analysis is shown below. Locate the test statistic and p-value on the printout. (Note: For large samples, z ≈ t.)

e. Give the appropriate conclusion in the words of the problem.

Question: Water distillation with solar energy. In countries with a water shortage, converting salt water to potable water is big business. The standard method of water distillation is with a single-slope solar still. Several enhanced solar energy water distillation systems were investigated in Applied Solar Energy (Vol. 46, 2010). One new system employs a sun-tracking meter and a step-wise basin. The new system was tested over 3 randomly selected days at a location in Amman, Jordan. The daily amounts of distilled water collected by the new system over the 3 days were 5.07, 5.45, and 5.21 litres per square meter ( l / m2 ). Suppose it is known that the mean daily amount of distilled water collected by the standard method at the same location in Jordan is µ = 1.4 / I m2.

a. Set up the null and alternative hypotheses for determining whether the mean daily amount of distilled water collected by the new system is greater than 1.4.

b. For this test, give a practical interpretation of the value α = 0.10.

c. Find the mean and standard deviation of the distilled water amounts for the sample of 3 days.

d. Use the information from part c to calculate the test statistic.

e. Find the observed significance level (p-value) of the test.

f. State, practically, the appropriate conclusion.

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free