Question

QUESTION 2

1. Now suppose Joyce doesn't have population standard deviation (perhaps because these are new machines); she only has her sample standard deviation which is 12. Using the same information, (500 grams average, sample mean of 495, sample size of 24), what are the results of Joyce's analysis? (Check all that apply.) You will need to use one of the tables available on Blackboard (knowing which one is part of the question).

   		Fail to reject the null hypothesis.
   		Reject the null hypothesis at 90% confidence.
   		Reject the null hypothesis at 95% confidence.
   		Reject the null hypothesis at 99% confidence.

20 points   

QUESTION 3

1. Bryce works for Big Cheese Wheel, a cheese company as a quality control manager. Usually, 3% of cheese is bad enough and has to be thrown out. Bryce's new hire, Rachel, found just 1% of cheese is bad (based on testing 205 lbs of cheese). Bryce wonders if Rachel is making mistakes (claiming bad cheese is actually good) or if this is just random and uses a hypothesis test to answer this question. To three decimal places, what is the calculated value of Bryce's hypothesis test?

10 points   

QUESTION 4

1. Using your answer from the previous question, is this statistically significant (note this is a two-tailed test)?

   		Yes, at the 95% level
   		Yes, at the 99% level
   		Yes, at the 99.9% level
   		It is not statistically significant

10 points   

QUESTION 5

1. The average 60-watt (a unit of power) bulb emits about 800 lumens (a measure of brightness) of light. Suppose the population standard deviation is 30 lumens. Also suppose you're testing a new watt bulb to see if it emits more light with the same 60 watts of power. With a sample of 100 bulbs and 99% confidence, what is the minimum average your sample can have and still be counted as statistically significant?

20 points   

QUESTION 6

1. Cassidy wants to know how little excersice someone can do and still lose weight. Suppose she gets 24 volunteers to do 20 minutes of walking a day for a week. She weighs them before and after the week in question and discovers they lost an average of ten pounds with a sample standard deviation of 18. At 99% significance, what was the result of the test?

   		Not statistically significant because the calculated score was less than the critical score.
   		Not statistically significant because the calculated score was greater than the critical score.
   		Statistically significant because the calculated score was less than the critical score.
   		Statistically significant because the calculated score was greater than the critical score.

Answer 1

Solution:

2) For question (2) provide the previous question also in which information about this question is given.

3) The null and alternative hypotheses are as follows:

H_{​​​​​​0} : P = 3% = 0.03 i.e. The population proportion of bad cheese is 0.03.

H_{​​​​​1} : P ≠ 0.03 i.e. The population proportion of bad cheese is not equal to 0.03.

To test the hypothesis we shall use z-test for single proportion. The test statistic is given as follows:

Where, p is sample proportion, P is hypothesized value of population proportion, Q = 1 - P and n is sample size.

Sample proportion of bad cheese is, p = 1% = 0.01

P = 0.03, Q = 1 - 0.03 = 0.97 and n = 205

The value of the test statistic is -1.679

4) For two-tailed test we make decision rule as follows:

If |Z| > Z_{(1- α}​​​​​​_/2) then we reject the null hypothesis and conclude that it is significant at α significance level.

If |Z| < Z_{(1- α}​​​​​​_/2) then we fail to reject the null hypothesis and conclude that it is not significant at α significance level.

We have, |z| = 1.679 (from question (3))

At 95% confidence level, α = 100 - 95 = 5% = 0.05.

At α = 0.05, Z_{(1- α}​​​​​​_/2) = Z_{(1- 0.05/2)} = 1.96

Since,  |Z| < Z_{(1- 0.05/2)}, therefore we shall be fail to reject the null hypothesis and conclude that it is not significant at 95% confidence level.

At 99% confidence level, α = 100 - 99 = 1% = 0.01

At α = 0.01, Z_{(1- α}​​​​​​_/2) = Z_{(1- 0.01/2)} = 2.58

Since,  |Z| < Z_{(1- 0.01/2)}, therefore we shall be fail to reject the null hypothesis and conclude that it is not significant at 99% confidence level.

At 99.9% confidence level, α = 100 - 99.9 = 0.1% = 0.001.

At α = 0.001, Z_{(1- α}​​​​​​_/2) = Z_{(1- 0.001/2)} = 3.29

Since,  |Z| < Z_{(1- 0.001/2)}, therefore we shall be fail to reject the null hypothesis and conclude that it is not significant at 99.9% confidence level.

Hence, the 4th option is correct which states that " It is not statistically significant".