Using traditional methods it takes 8.2 hours to receive a basic flying license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique on 26 students and observed that they had a mean of 8.0 hours with a variance of 2.89. Is there evidence at the 0.1 level that the technique reduces the training time? Assume the population distribution is approximately normal.Step 3 of 5:Specify if the test is one-tailed or two-tailed.

Question
Asked Dec 8, 2019
1 views

Using traditional methods it takes 8.2 hours to receive a basic flying license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique on 26 students and observed that they had a mean of 8.0 hours with a variance of 2.89. Is there evidence at the 0.1 level that the technique reduces the training time? Assume the population distribution is approximately normal.

Step 3 of 5:

Specify if the test is one-tailed or two-tailed.

check_circle

Expert Answer

Step 1

Null hypothesis:

µ=8.2.

Alternative hypothesis:

µ<8.2.

This is a left tailed test.

Since the population standard deviation is unknown, the appropriate test is one sample t-test.

Here, the sample mean, x-bar is 8.

Population mean, µ is 8.2.

Sample variance, σ2 = 2.89.

Sample standard deviation, σ = 1.7.

Sample size, n is 26.

The test statistic value can be obtained as follows:

help_outline

Image Transcriptionclose

t = In 8 – 8.2 1.7 V26 x -1.667 ||

fullscreen
Step 2

Computation of P-value:

The P-value for the left tailed t-value at 25 degrees of freedom is –1.667 is 0.054 which can be can be obta...

help_outline

Image Transcriptionclose

=T.DIST(-1.667,25,TRUE) 0.053997729

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Statistics

Hypothesis Testing

Related Statistics Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: Use the t-distribution and the sample results to complete the test of the hypotheses. Use a 5% signi...

A: Given,Significance level 5%, and also x-=4.8, s=2.3 with n=15.Null and alternative hypothesis,

question_answer

Q: A poll was conducted to investigate opinions about global warming. The respondents who answered yes ...

A: The appropriate null and alternative hypotheses are stated below:H0: The sex of the respondent and t...

question_answer

Q: Construct the indicated confidence interval for the difference between population proportions P1 - P...

A: Confidence interval:The (1-α)100 % confidence interval for proportion p1 – p2 is given by,

question_answer

Q: Assume a significance level of a = 0.05 and use the given information to complete parts (a) and (b) ...

A: Decision rule:If p-value ≤ α, then reject the null hypothesis. Otherwise, fail to reject the null hy...

question_answer

Q: The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.66 milli...

A: Given DataMean = 5.66Standard Deviation = 0.03Top 9 % is given by Finding the Z-value corresponding ...

question_answer

Q: 10

A: Given DataMoment Generating function of X is 

question_answer

Q: According to Inc.com, 79% of job seekers used social media in their job search in 2018. Many believe...

A: (a) Null hypothesis: H0: p≤0.79. Alternative hypothesis: Ha: p&gt;0.79. From the given information, ...

question_answer

Q: Assume that a sample is used to estimate a population mean μμ. Find the 99.5% confidence interval fo...

A: IntroductionThe 100 (1 – α) % confidence interval for the population mean, μ, for given sample stand...

question_answer

Q: Given the linear correlation coefficient r and the sample size n, determine the critical values of r...

A: The critical value is obtained below:From the given information the value of correlation is (r) = 0....