Statistics Tutorials: How to solve Hypothesis Testing Problems
One common type of problem you will find in Basic Statistics homework is the type of problem that involves using sample data to test an hypothesis.
A hypothesis is a statement about a population parameter. This is, it is a claim that we make about a certain population parameter, such as the population mean, or the population standard deviation.
For example, an engineer from a car manufacturer may claim that the population mean gas mileage of a new car model is 25 mpg. That would be an hypothesis. Or for example, a political polls researcher may claim that the voting share of certain candidate is 53%. That would be another hypothesis, about the true proportion of voters who support that certain candidate.
Consider the following example: A psychologist claims that the mean IQ scores of statistics instructors is greater than 100. She collects sample data from 15 statistics instructors and she finds that \(\bar{X}=118\) and s = 11. The sample data appear to come from a normally distributed population with unknown \(\mu\) and \(\sigma\).
Let us solve this problem:
Notice that we want to test the following null and alternative hypotheses
\[\begin{align}{{H}_{0}}:\mu {\le} {100}\, \\ {{H}_{A}}:\mu {>} {100} \\ \end{align}\]
Considering that the population standard deviation \(\sigma\) is not provided, we have to use a ttest with the following formula:
\[t =\frac{\bar{X}\mu }{s / \sqrt{n}}\]
This corresponds to a righttailed ttest. The tstatistics is given by the following formula:
\[t=\frac{\bar{X}\mu }{s /\sqrt{n}}=\frac{{118}100}{11/\sqrt{15}}={6.3376}\]
The critical value for \(\alpha = 0.05\) and for \(df = n 1 = 15 1 = 14\) degrees of freedom for this righttailed test is \(t_{c} = 1.761\). The rejection region is given by
\[R = \left\{ t:\,\,\,t>{ 1.761 } \right\}\]
Since \(t = 6.3376 {>} t_c = 1.761\), then we reject the null hypothesis H_{0}.
Alternatively, we can use the pvalue approach. The righttailed pvalue for this test is calculated as
\[p=\Pr \left( {{t}_{14}}>6.3376 \right)=0.000\]
Considering that the pvalue is such that \(p = 0.000 {<} 0.05\), we reject the null hypothesis H_{0}.
Hence, we have enough evidence to support the claim that the mean IQ scores of statistics instructors is greater than 100.

Submit your problems for a free quote and we will be back shortly (a couple of hours max). It costs you NOTHING to find out how much it would cost to solve your problems.
We provide a quality problem solving service on the following stats topics:
 Probability
 Basic Concepts: Sample Space, Events.
 Densities and Distributions.
 Descriptive statistics.
 Descriptive Analysis of data.
 Graphs and charts.
 Inferential Statistics
 Means, variances, populations, samples.
 Intervals of Confidence.
 Ztest, Ttest and Ftests.
 Hypothesis Testing.
 ANOVA.
 Correlation.
 Linear and nonlinear regression.
 Nonparametric Statistics.
 Sign Test.
 Wilkinson Tests.
 KruskalWallis Test.
 Spearman Correlation Coefficient.
Our team is highly experienced in SPSS, Minitab, EXCEL and the majority of the statistical software packages out there. Request your free quote. We a have a satisfaction guarantee policy. If you're not satisfied, we'll refund you. Please see our terms of service for more information about the satisfaction guaranteed policy. See also a sample of our work.
Why we can help with your Stats?
Experience
We have successfully help customers online for more than 10 years now
Statistics Expertise
We can do handle any type of statistics analyis/homework/questions. Our tutors have real expertise, and big majaority of our customers are returning customers
StepbyStep Solutions
We provide detailed, stepbystep solutions, and we strive to provide exactly what our customers want.
Free Quote
Email us your problems, we will review them and promptly come back to you with a free quote
Very Competitive Prices
We strive to provide the best possible prices for our services
We take pride of our work
Our tutors take pride on the work we do. We diligenty do work for our customers, and put great attention to details striving to always provide a great final product