Explanation Calculation: It is given that the sample size n = 65 , sample mean x ¯ = 38.16 and the population standard deviation σ = 5.95 . In this context, the parameter of interest is population mean. Because the researcher interested to test the population mean. However, the value of σ is known, so, the z -test is appropriate. Assumptions for performing a hypothesis test about μ when σ is known: • The samples taken from the population are simple random samples. • The sample size should be large that is, n > 30 or the population should be distributed normally. Requirement check: • The sample of 65 was selected at random. • The sample size of 65 is greater than 30, that is, 65 > 30 . Thus, the condition is satisfied. Step 1: Denote μ as true population mean. The test hypotheses are given below: Null hypothesis: H 0 : μ = 40 That is, the true population mean is 40 . Alternative hypothesis: H 1 : μ < 40 That is, the true population mean is less than 40 . Step 2: It is given that the level of significance is 0.01. Step 3: Test statistic: The t- test statistic is: t = x ¯ − μ σ n , Where, x ¯ be the sample mean, μ be the hypothesized mean and σ be the standard deviation and n be the sample size

2nd Edition

ISBN: 9781259570643

Author: Navidi

Publisher: MCG

See similar textbooks

Concept explainers

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of tw…

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency o…

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow compar…

Videos

Question

Chapter 8.5, Problem 4CYU

To determine

Identify the parameter of interest.

Check whether it can be concluded that the population mean is less than 40 at the level of significance α=0.01.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.5, Problem 3CYU

Chapter 8.5, Problem 5E

Students have asked these similar questions

A company manages an electronic equipment store and has ordered 200200 LCD TVs for a special sale. The list price for each TV is $200200 with a trade discount series of 6 divided by 10 divided by 2.6/10/2. Find the net price of the order by using the net decimal equivalent.

According to flightstats.com, American Airlines flights from Dallas to Chicago are on time 80% of the time. Suppose 10 flights are randomly selected, and the number of on-time flights is recorded. (a) Explain why this is a binomial experiment. (b) Determine the values of n and p. (c) Find and interpret the probability that exactly 6 flights are on time. (d) Find and interpret the probability that fewer than 6 flights are on time. (e) Find and interpret the probability that at least 6 flights are on time. (f) Find and interpret the probability that between 4 and 6 flights, inclusive, are on time.

Show how you get critical values of 1.65, -1.65, and $1.96 for a right-tailed, left- tailed, and two-tailed hypothesis test (use a = 0.05 and assume a large sample size).

Chapter 8 Solutions

Essential Statistics

Ch. 8.1 - Check Your Understanding 1. Last year, the mean...Ch. 8.1 - Prob. 2CYU Ch. 8.1 - Prob. 3CYU Ch. 8.1 - Prob. 4CYU Ch. 8.1 - Prob. 5CYU Ch. 8.1 - Prob. 6CYU Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - In Exercises 9–12, determine whether the statement...

Knowledge Booster

$Statistics$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Identify the parameter of interest. Check whether it can be concluded that the population mean is less than 40 at the level of significance α = 0.01 .

Concept explainers

Videos

Identify the parameter of interest. Check whether it can be concluded that the population mean is less than 40 at the level of significance α=0.01.

Want to see the full answer?

Chapter 8 Solutions

Identify the parameter of interest.

Check whether it can be concluded that the population mean is less than 40 at the level of significance α=0.01.