GATE (TF) Textile 2016 Question Paper Solution | GATE/2016/TF/17

Question 17 (Textile Engineering & Fibre Science)

The test statistic to be used for carrying out a test of hypothesis on the mean of a normal distribution with unknown variance is

(C)\chi ^2
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What is a hypothesis test in statistics example?

A hypothesis test is a statistical method used to determine whether a hypothesis about a population parameter is supported by sample data. Here’s an example:
Suppose a company claims that the average weight of their product is 5 pounds. To test this claim, a sample of 50 products is randomly selected, and their weights are measured. The sample mean is found to be 4.8 pounds, with a standard deviation of 0.4 pounds.
To conduct a hypothesis test, we need to state the null hypothesis and alternative hypothesis. The null hypothesis (denoted as H0) is the statement we want to test, while the alternative hypothesis (denoted as Ha) is the opposite statement.
In this example, the null hypothesis is that the population mean weight of the product is 5 pounds (H0: μ = 5), and the alternative hypothesis is that the population mean weight is less than 5 pounds (Ha: μ < 5).
Next, we need to choose a significance level (denoted as α), which is the probability of rejecting the null hypothesis when it is actually true. Suppose we choose α = 0.05.
Using a one-sample t-test with a significance level of 0.05, we calculate the t-statistic:
t = (4.8 – 5) / (0.4 / sqrt(50)) = -2.236
The degrees of freedom for the t-test is n-1, which is 49 in this case.
We then look up the t-value on a t-distribution table with 49 degrees of freedom and a significance level of 0.05. The critical value is -1.677, which is the t-value that corresponds to the area of 0.05 in the left tail of the t-distribution.
Since our calculated t-value of -2.236 is less than the critical value of -1.677, we can reject the null hypothesis at the 0.05 significance level. This means that there is sufficient evidence to conclude that the population mean weight of the product is less than 5 pounds.

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