Question

(1 point) Calvin thinks a certain potato chip maker is putting fewer chips in their regular bags of chips. From a random sample of 23 bags of potato chips he calculated a P value of 0.135 for the sample. (a) At a 5% level of significance, is there evidence that Calvin is correct? (Type: Yes or No): (b) At a 10% level of significance, is there evidence that he is correct? (Type: Yes or No): (c) In a statistical test of hypotheses, we say that the data are statistically significant at level αα if A. the P - value is less than αα. B. the P - value is larger than αα. C. αα is small. D. α=0.05α=0.05.

Answer 1

a) Yes, there is evidence that Calvin's claim is correct.

b) Yes, there is evidence that Calvin's claim is correct.

c) Option A is correct.

In a statistical test of hypothesis, we say that the data are statistically significant at level α if the P - value is less than α.

Explanation:

The first step in any hypothesis testing is to state the null and alternative hypothesis.

The null hypothesis for this question would be that the potato chip maker is putting fewer chips in their regular bags of chips

And the alternative hypothesis would be that the potato chip maker is not putting fewer chips in their regular bags of chips; the potato chip maker is putting more or equal amount of chips in their regular bags of chips.

Let k = the amount of chips in their regular bags of chips.

Mathematically,

Null hypothesis

H₀: μ₀ < k (Calvin's claim)

Alternative hypothesis

Hₐ: μ₀ ≥ k

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for the questions,

a) p-value = 0.135

significance level = 5% = 0.05

0.135 > 0.05

p-value > significance level

Hence, we do not reject the null hypothesis. And yes, there is evidence that Calvin's claim is correct.

b) p-value = 0.135

significance level = 10% = 0.10

0.135 > 0.10

p-value > significance level

Hence, we do not reject the null hypothesis. And yes, there is evidence that Calvin's claim is correct.

c) Statistical significance is the likelihood that a relationship between two or more variables is caused by something other than chance.

A data set is said to have statistical significance when the p-value is less than the significance level and the alternative hypothesis has to be accepted.

Hope this Helps!!!