n independent knowledge, attitudes and practices survey on COFLU-20 was conducted in a large first-world country. The individual attitude scores were found to be normally distributed with the mean of 5 and a standard deviation of 1.3. For our current investigation of the 300 respondents, the mean score for attitude was found to be 5.6 with a standard deviation of 2.8 The researcher has asked you to use a 3% level of significance, to test whether the population mean score for attitude towards COFLU-20 is significantly different from 5. To conduct this test, you are required to: (d) Calculate the value of the test statistic for this test. (e) Calculate the p-value for this test. (f) Using the p-value approach, state the conclusion of this test. State your reasoning for arriving at your conclusion.
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 two parameters.
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 or measure of central tendency is a central or typical value for a probability distribution.
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 comparison between two scores that belong to different normal distributions.
n independent knowledge, attitudes and practices survey on COFLU-20 was conducted in a large first-world country. The individual attitude scores were found to be
The researcher has asked you to use a 3% level of significance, to test whether the population mean score for attitude towards COFLU-20 is significantly different from 5. To conduct this test, you are required to:
(d) Calculate the value of the test statistic for this test.
(e) Calculate the p-value for this test.
(f) Using the p-value approach, state the conclusion of this test. State your reasoning for arriving at your conclusion.
From the provided information,
The hypotheses can be constructed as:
Null hypothesis: H0: µ = 5
Alternative hypothesis: H1: µ ≠ 5
Sample size (n) = 300
Sample mean (x̄) = 5.6
Sample standard deviation (s) = 2.8
Population standard deviation (σ) = 1.3
The level of significance (α) = 0.03
a)
The population standard deviation is known therefore, the z distribution will be used.
The value of the test statistic can be obtained as:
Step by step
Solved in 3 steps with 1 images
