Purchase Solution

Hypothesis Testing, Confidence Intervals and Levels of Significance

Not what you're looking for?

Ask Custom Question

In a statistics lecture, students are asked whether or not they enjoyed doing statistics. Random sample of 50 students was taken and 30 of them said that they enjoyed doing statistics. The lecturer claimed that more than 50% of the students enjoyed doing statistics.

(i) Test, at the 5% level of significance, whether or not the lecturer's claim is reasonable. State the null and alternative hypotheses of the test.

(ii) Find a 95% and a 99% confidence intervals for the true proportion of students who enjoyed doing statistics. Which one is wider? Why?

(iii) If the lecturer would like the difference between the true proportion and the sample
proportion to be less than 5%, what is the minimum number of students he should ask Use alpha = 0.05

Purchase this Solution

Solution Summary

Hypothesis testing, confidence intervals and levels of significance are investigated.

Solution Preview

First, we need to find the sample mean of the proportion of students who enjoyed doing statistics.
p-hat=x/n=30/50=0.60
Note. The sample size n=50.

(i) Hypotheses.

Null hypothesis H0: p=0.50
Alternative hypothesis Ha: p>0.50

Use z-test. We can calculate the z-statistic
z=(p-hat-0.50)/sqrt[0.50*(1-0.50)/n]
=(0.60-0.50)/sqrt[0.5*0.5/50]=1.4142

At the 5% level of significance, the critical value ...

Solution provided by:
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
Purchase this Solution


Free BrainMass Quizzes
Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.

Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.

Know Your Statistical Concepts

Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.

Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.