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 49bags of flour for evaluation and finds that they contain an average of 76.5insect parts per 100 grams.Test to see if the entire shipment of wheat is not fit for human consumption.Test the claim using a 5% level of significance.Give answer to at least 4 decimal places.

What are the correct hypotheses?

H_0:

H_1:

Based on the hypotheses, find the following:

Test Statistic z = p-value =

Based on the above we choose to:

1. Accept the null hypotheseis
2. Accept the alternative hypothesis
3. Reject the null hypothesis
4. Fail to reject the null hypothesis

The correct summary would be:

1. There is not enough evidence to support the claim
2. There is not enough evidence to reject the claim
3. There is enough evidence to reject the claim
4. There is enough evidence to support the claim

What is the type I error in this situation?

1. The FDA says the flour is fit for consumption, but there really was more than 75 insects parts in the flour
2. The FDA believes the flour is contaminated when it really is not.

2. The time to complete the Advanced Placement (AP) Statistics Exam in previous years is normally distributed with an average time of 2.6 hours. Because of school closures due to COVID-19, the College Board offered an at-home test for the 2020 AP Statistics Exam. A teacher feels that students, on average, will have a different completion time for the at-home exam. They take a random sample of 26 students that took the exam and their mean time was 2.67 hours with a standard deviation of 0.3 hours. Test to see if the mean time has significantly changed using a 10% level of significance. Give answers to at least 4 decimal places.

What are the correct hypotheses?

H₀:

H₁:

Based on the hypotheses, find the following: Test Statistic t = Critical-Value t =

Shade the sampling distribution curve with the correct critical value(s) and shade the critical regions. The arrows can only be dragged to t-scores that are accurate to 1 place after the decimal point (these values correspond to the tick marks on the horizontal axis).Select from the drop down menuto shade to the left, to the right, between or left and right of the t-score(s), then drag shaded area to match your critical value(s).

The correct decision is to:

1. Reject the null hypothesis
2. Fail to reject the null hypothesis
3. Accept the null hypothesis
4. Accept the alternative hypothesis

The correct summary would be:

1. There is enough evidence to support the claim
2. There is no enough evidence to reject claim
3. There is not enough evidence to support the claim
4. There is enough evidence to reject the claim

3. Testing: H0:41.5 H1:>41.5 Your sample consists of 45 values, with a sample mean of 42. Suppose the population standard deviation is known to be 2.19

• Calculate the value of the test statistic, rounded to 2 decimal places. z=

b) At=0.025, the rejection region is

• z>1.96
• z<-1.96
• z<-2.24 orz>2.24
• z<-1.96 orz>1.96
• z>2.24
• z<-2.24

c) The decision is to

• Reject the null hypothesis
• Fail to reject the null hypothesis
• Accept the alternative hypotheis
• Accept the null hypothesis

d) Suppose you mistakenly failed to reject the null hypothesis in this problem, what type of error is that?

• Type II
• Type I