Q4) A Professor wishes to analyse the marks obtained by the students of his class in an exam. He finds the mean of the marks of all students to be 75. However, a student believes the mean to be different. He analyses the marks of 7 students from the class and finds the mean to be 78 and standard deviation to be 10. (a) State the null and alternative hypotheses. (b) At a confidence interval of 99%, is there enough evidence to discard the null hypothesis? Use the p-value method.
Q4) A Professor wishes to analyse the marks obtained by the students of his class in an exam. He finds the mean of the marks of all students to be 75. However, a student believes the mean to be different. He analyses the marks of 7 students from the class and finds the mean to be 78 and standard deviation to be 10. (a) State the null and alternative hypotheses. (b) At a confidence interval of 99%, is there enough evidence to discard the null hypothesis? Use the p-value method.
Q4) A Professor wishes to analyse the marks obtained by the students of his class in an exam. He finds the mean of the marks of all students to be 75. However, a student believes the mean to be different. He analyses the marks of 7 students from the class and finds the mean to be 78 and standard deviation to be 10. (a) State the null and alternative hypotheses. (b) At a confidence interval of 99%, is there enough evidence to discard the null hypothesis? Use the p-value method.
A Professor wishes to analyse the marks obtained by the students of his class in an exam. He finds the mean of the marks of all students to be 75. However, a student believes the mean to be different. He analyses the marks of 7 students from the class and finds the mean to be 78 and standard deviation to be 10.
State the null and alternative hypotheses.
At a confidence interval of 99%, is there enough evidence to discard the null hypothesis? Use the p-value method.
Transcribed Image Text:Q4) A Professor wishes to analyse the marks obtained by the students of his class in an exam.
He finds the mean of the marks of all students to be 75. However, a student believes the mean
to be different. He analyses the marks of 7 students from the class and finds the mean to be 78
and standard deviation to be 10.
(a) State the null and alternative hypotheses.
(b) At a confidence interval of 99%, is there enough evidence to discard the null hypothesis?
Use the p-value method.
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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