It is believed that the average starting salary for a 21-25 year old college grad exceeds $52,000 per year. Hence, it is desired
to test H0: µ ≤ 52,000 versus H1 : µ > 52,000. Assume σ = $5,745 and a SRS of size 65 is taken. We reject H0 when X > 53,460. The significance level α is:
1 answer:
Answer:
The significance level α is 0.02.
Step-by-step explanation:
A hypothesis test for single mean can be performed to determine whether the average starting salary for a 21-25 year old college grad exceeds $52,000 per year.
The hypothesis is defined as follows:
<em>H₀</em>: The average starting salary for a 21-25 year old college grad does not exceeds $52,000 per year, i.e. <em>µ</em> ≤ 52,000.
<em>Hₐ</em>: The average starting salary for a 21-25 year old college grad exceeds $52,000 per year, i.e. <em>µ</em> > 52,000.
The information provided is:
<em>σ</em> = $5,745
<em>n</em> = 65
Also, if then the null hypothesis will be rejected.
Here, we need to compute the value of significance level <em>α</em>, the type I error probability.
A type I error occurs when we reject a true null hypothesis (H<em>₀</em>).
That is:
<em>α</em> = P (type I error)
<em>α</em> = P (Rejecting H<em>₀</em>| H<em>₀</em> is true)
*Use a <em>z</em>-table for the probability.
Thus, the significance level α is 0.02.
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Answer:
c) Is not a property (hence (d) is not either)
Step-by-step explanation:
Remember that the chi square distribution with k degrees of freedom has this formula
Where N₁ , N₂m .... are independent random variables with standard normal distribution. Since it is a sum of squares, then the chi square distribution cant take negative values, thus (c) is not true as property. Therefore, (d) cant be true either.
Since the chi square is a sum of squares of a symmetrical random variable, it is skewed to the right (values with big absolute value, either positive or negative, will represent a big weight for the graph that is not compensated with values near 0). This shows that (a) is true
The more degrees of freedom the chi square has, the less skewed to the right it is, up to the point of being almost symmetrical for high values of k. In fact, the Central Limit Theorem states that a chi sqare with n degrees of freedom, with n big, will have a distribution approximate to a Normal distribution, therefore, it is not very skewed for high values of n. As a conclusion, the shape of the distribution changes when the degrees of freedom increase, because the distribution is more symmetrical the higher the degrees of freedom are. Thus, (b) is true.