Question
1. The Food and Drug Administration (FDA) is a U.S. government agency that regulates (you guessed it) food and drugs for consumer safety. One thing
1. The Food and Drug Administration (FDA) is a U.S. government agency that regulates (you guessed it) food and drugs for consumer safety. One thing the FDA regulates is the allowable insect parts in various foods. You may be surprised to know that much of the processed food we eat contains insect parts. An example is flour.
When wheat is ground into flour, insects that were in the wheat are ground up as well. The mean number of insect parts allowed in 100 grams (about 3 ounces) of wheat flour is 75. If the FDA finds more than this number, they conduct further tests to determine if the flour is too contaminated by insect parts to be fit for human consumption. The population standard deviation is 11.
The FDA cannot afford to sample the entire shipment so they take a random sample of 40bags of flour for evaluation and finds that they contain an average of 75.7insect parts per 100 grams.Test to see if the entire shipment of wheat is not fit for human consumption.Test the claim using a 1% level of significance.Give answers to at least 4 decimal places.
What are the correct hypotheses?
- H0: Select an answer: p x s s p = > < insect parts/100 grams
- HA: Select an answer p s x s p = > < insect parts/100 grams
Based on the hypotheses, find the following:
- Test Statistic z =
- p-value =
- Based on the above we choose to Select an answer: Accept the null hypothesis, Accept the alternative hypotheis, Fail to reject the null hypothesis, Reject the null hypothesis
- The correct summary would be Select an answer: There is not enough evidence to reject the claim, There is enough evidence to support the claim, There is enough evidence to reject the claim, There is not enough evidence to support the claim,_____ that the entire shipment of wheat is not fit for human consumption.
2. The mean age when smokers first start is 13 years old with a population standard deviationof 1.8 years. A researcher thinks that smoking age has significantly changed since the invention of ENDSelectronic nicotine delivery systems. A survey of smokers of this generation was done to see if the mean age has changed. Thesample of 30 smokers found that their mean starting age was 12.4 years old. Do the data support the claim at the 1% significance level?
What are the correct hypotheses?
- H0: Select an answer: s p p s x < = > years
- HA: Select an answer: p s s x p > = < years
Based on the hypotheses, find the following:
- Test Statistic z = (Give answer to at least 4 decimal places)
- p-value = (Give answer to at least 4 decimal places)
- Based on the above we choose to Select an answer: Fail to reject the null hypothesis, Accept the alternative hypotheis, Reject the null hypothesis, Accept the null hypothesis
- The correct summary would be: Select an answer: There is enough evidence to support the claim, There is not enough evidence to support the claim, There is enough evidence to reject the claim, There is not enough evidence to reject the claim, that the claim that the mean age smokers first start is different than 13.
3. The weights of newborn children in the United States vary according to the normal distribution with mean 7.5 pounds and standard deviation 1.25 pounds. An article in the The Wall Street Journalclaims that the average birth weight is decreasing over time.
A local hospital wanted to see if the claim was true and randomly sampled 19 baby's weights and found an average weight of 7.4 pounds.Test the claim using a 1% level of significance that the mean weight significantly smaller than the national average of 7.5pounds. Use the population standard deviation of1.25 pounds.Give answer to at least 4 decimal places.
What are the correct hypotheses? (Select the correct symbols.)
- H0: Select an answer: p s x s p < > = pounds
- HA: Select an answer: s p p s x > = < pounds
Based on the hypotheses, find the following:
- Test Statistic =
- p-value =
- The correct decision is to Select an answer: Fail to reject the null hypothesis, Accept the null hypothesis, Accept the alternative hypotheis, Reject the null hypothesis
- The correct summary would be Select an answer: There is enough evidence to support the claim, There is not enough evidence to support the claim, There is not enough evidence to reject the claim, There is enough evidence to reject the claim that the mean weight significantly smaller than the national average of 7.5pounds.
4. The mean age when smokers first start is 13 years old with a population standard deviationof 2 years. A researcher thinks that smoking age has significantly changed since the invention of ENDSelectronic nicotine delivery systems. A survey of smokers of this generation was done to see if the mean age has changed. Thesample of 31 smokers found that their mean starting age was 12 years old. Do the data support the claim at the 10% significance level?
What are the correct hypotheses?
- H0: Select an answer: p s p s x = > < years
- HA: Select an answer: s x s p p > < = years
Based on the hypotheses, find the following:
- Test Statistic z = (Give answer to at least 4 decimal places)
- Critical Values = (Give answer to at least 4 decimal places)
- Based on the above we choose to Select an answer: Reject the null hypothesis, Accept the alternative hypotheis, Accept the null hypothesis, Fail to reject the null hypothesis
- The correct summary would be Select an answer: There is not enough evidence to support the claim, There is enough evidence to support the claim, There is not enough evidence to reject the claim, There is enough evidence to reject the claim that the claim that the mean age smokers first start is different than 13.
5. The manufacturer of a particular brand of tires claims they average at least 80,000 km before needing to be replaced. From past studies of this tire, it is known that the population standard deviation is 13,000 km.
A survey of tire owners was conducted to determine if the mileage of the tires is lower than 80,000 km. From the 39 tires sampled, the mean lifespan was 78,000 km. Testing at = 8%, can we prove that the data is inconsistent with the manufacturers claim?
- what test should we use a t or z?
- What are the correct hypotheses? H0H0: Select an answer: s p p s x < = > HAHA: Select an answer: p s s x p = < >
- Test Statistic =
- Critical Value = (note the direction of HAHA)
- The correct decision is to Select an answer: Fail to reject the null hypothesis, Reject the null hypothesis, Accept the null hypothesis, Accept the alternative hypotheis .
- The correct conclusion would be:
- There is not enough evidence to conclude that the tires last less than the kilometres claimed
- There is not enough evidence to conclude that the tires do not last less than the kilometres claimed
- There is enough evidence to conclude that the tires do not last less than the kilometres claimed
- There is enough evidence to conclude that the tires last less than the kilometres claimed
6. The overall mean throwing distance of a football for Levi, a high school freshman quarterback, is 37 yards with a population standard deviation of 16.1 yards. The team coach tells Levi to adjust their grip to get more distance. The coach records the distances for 21 throws and finds the mean distance to be 42 yards. The coach thought the different grip helped Levi throw further than 37 yards. Test the coach's claim using a 5% level of significance. Give answer to at least 4 decimal places.
- What are the correct hypotheses? H0: Select an answer: s p s p x = > < yards HA: Select an answer: x p s s p < > = yards
Based on the hypotheses, find the following:
- Test Statistic =
- Critical-value =
- The correct decision is to Select an answer:: Accept the alternative hypotheis, Fail to reject the null hypothesis, Accept the null hypothesis, Reject the null hypothesis
- The correct summary would be: Select an answer There is not enough evidence to reject the claim, There is enough evidence to support the claim, There is enough evidence to reject the claim, There is not enough evidence to support the claim that the population mean distance is significantly more than 37 yards.
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