Suppose that we have two different data sets. The first data set has size n1  =  76 observations and the second data set has n2  =  97 observations. Suppose that we use the first data set to test some hypothesis at the 2% significance level, and then we use the second data set to test some other hypothesis at the 9% significance level. Suppose that both null hypotheses are true, and that the hypothesis tests are independent. What is the probability of making at least one Type I error?

Q: are conducting a study to see if the accuracy rate for fingerprint identification is significantly…

A: A hypothesis is said to be left tailed, if the population parameter is less than some hypothesized…

Q: A national publishing house claims that 45% of all weekly magazine readers in South Africa read…

A: Given: House claims 45% of weekly magazine The significance level is 5% The magazine readers are 500…

Q: Suppose you toss a coin (heads or tails) three times. The prior probability of the hypothesis H that…

A: H : The coin is double headed E : Three heads in three tosses So, P(E|H) = 1 [as the coin is double…

Q: A company manager wants to compare the satisfaction levels of his customers from two stores…

A:

Q: Researcher A uses a sample of n = 100 for their hypothesis test while Researcher B uses a sample of…

A: Standard error is the error due to random sampling. Population is the set of all objects of…

Q: ​If, in a sample of n=25 selected from a normal​ population, X=52 and S=10​, what is the value of…

A:

Q: Suppose that in a random selection of 100 colored candies, 25% of them are blue. The candy company…

A:

Q: A researcher administers a treatment to a sample of participants selected from a population with µ =…

A: A researcher administers a treatment to a sample of participants selected from a population with µ =…

Q: Suppose we want to test the null hypothesis H0 : p = 0.60 against the alternative hypothesis Ha : p…

A: Given that  Null hypothesis H0: P=0.60 Alternative hypothesis H1: P<0.60   [ Left tailed test ]…

Q: A fair six-sided dice has the number 1 on one face, the number 2 on two faces and the number 3 on…

A: Given that dice has: 1 - on one face 2 -  on two faces 3 -  on three faces

Q: Suppose that in a random selection of 100 colored​ candies, 21​% of them are blue. The candy company…

A: Suppose that in a random selection of 100 colored​ candies, 21​% of them are blue. The candy company…

Q: In a two-sample t-test, suppose you obtain sample means equal to 25 in sample 1, and 26 in sample 2.…

A: Given that  sample means equal to 25 in sample 1, and 26 in sample 2.

Q: It is known that 51% of American college students fail a course during their freshman year. A…

A: Given: P = 0.51 n = 9 X = 3 Formula Used: Test-statistic Z = p^-PP(1-P)n

Q: Suppose that in a random selection of 100 colored candies, 27% of them are blue. The candy company…

A: State the hypotheses. That is, the percentage of blue candies is equal to 0.29. That is, the…

Q: A national publishing house claims that 35% of all weekly magazine readers inSouth Africa read their…

A: Null Hypothesis: H0: The proportion of all weekly magazine readers in South Africa read their…

Q: A researcher conducts a research study to examine whether there is a difference between two…

A: A null hypothesis is a type of hypothesis used in statistics that indicates that there is no…

Q: If a sample of 100 people is chosen from a town of​ 100,000 people without​ replacement, is it…

A: In this case a sample of 100 people of chosen without replacement from a town of 100,000 people.

Q: 2. A random sample of 500 registered voters in Phoenix is asked if they favor the use of oxygenated…

A: Solution True probability is 0.75

Q: In a 300-person focus group, 60% of participants like durian. It turns out that people who like…

A: Given information: n = 300 Number of people who like durian=0.60*300=180Number of people who do not…

Q: Suppose a sample size of 103 was used to conduct a left tailed hypothesis test for a single…

A: Given Information:  Sample size (n) = 103  Hypothesis: Ho: u = 22  p-value = 0.04

Q: It is claimed that the proportion of high school athletes who go on to play sports in college is…

A: We have given the following interpretation.   A claimed that the proportion of high school athletes…

Q: a 0.45 chance of concluding a deal to export agri- cultural equipment to a developing nation if a…

A: Consider A as the event that the deal is happening and B as the event the major competitor bid for…

Q: Norman is performing a hypothesis test in which he rejects the null hypothesis at a significance…

A: Given that  Norman is performing a hypothesis test in which he rejects the null hypothesis H0. Level…

Q: A teacher is comparing the mean study time of his freshmen and senior students. He believes that his…

A:

Q: Identify the null and alternative hypotheses for this test. Choose the correct answer below.

A:

Q: The table to the right gives a breakdown of the root causes of a sample of 79 industrial accidents.…

A:

Q: health provider saw that 48% of their members received their flu shot in recent years. The health…

A: Hypothesis testing plays a major role in research and development. To diagnose the underlying cause…

Q: Suppose that in a random selection of 100 colored​ candies, 22​% of them are blue. The candy company…

A:

Q: Suppose that in a random selection of 100 colored candies, 26% of them are blue. The candy company…

A: Solution: Given information: n= 100 Sample size  p^= 0.26  Sample proportion p= 0.23 Population…

Q: Suppose we want to test the null hypothesis H0 : p = 0.34 against the alternative hypothesis H1 : p…

A: Solution Given hypothesis H0 : p = 0.34 against H1 : p < 0.34 Sample=x=120 N = 300 P(cap) =…

Q: Suppose that in a random selection of 100 colored candies, 22% of them are blue. The candy company…

A: From the provided information, The hypotheses can be constructed as: H0: p = 0.28 H1: p ≠ 0.28…

Q: In hypothesis testing, such as testing the difference between two population proportions, which of…

A: A hypothesis test is decision-making about a population parameter. Here we make decisions based on…

Q: A hypothesis test was conducted to test whether more than​ 50% of recent college graduates had a job…

A: Claim: Test whether more than​ 50% of recent college graduates had a job offer prior to graduation.…

Q: Norman is performing a hypothesis test in which he rejects the null hypothesis at a significance…

A: Norman is performing a hypothesis test in which he rejects the null hypothesis at a significance…

Q: The p-value is the probability of obtaining a sample mean that is at least as extreme as the one…

A: To find whether the given statement is true or false.

Q: Suppose that in a random selection of 100 colored candies, 25% of them are blue. The candy company…

A:

Q: Suppose that in a random selection of 100 colored​ candies, 23​% of them are blue. The candy company…

A: Given that, p^=0.23,P=0.28,n=100 The null and alternative hypothesis is, Hence, the correct answer…

Q: . A consumer.research firm reports that the 95% confidence interval for the proportion of consumers…

A: Denote p as the true proportion of consumers, who prefer brand K tissue.

Q: If you use a 0.03 level of significance in a​ (two-tail) hypothesis​ test, what is your decision…

A: Given info: level of significance: α=0.03 Tail of the hypothesis​ test: two-tail   Hypotheses: H0:…

Q: Suppose that in a random selection of 100 colored candies, 25% of them are blue. The candy company…

A: From the provided information, Sample size (n) = 100 Sample proportion (p̂) = 0.25 Level of…

Q: A recent article in a university newspaper claimed that the proportion of students who commute more…

A: Claim : The proportion of students who commute more than 15 miles to school is no more than 20%. Let…

Q: d. How many animals should be included in the study to repeat the test with the same significance as…

A: (d) Number of cats in the shelter = 100 Number of dogs in the shelter = 50 no of old cats in the…

Q: Suppose that in a random selection of 100 colored candies, 25% of them are blue. The candy company…

A: Given: p0=0.27, n=100 and p^=0.25.   Then, the test statistic…

Q: Suppose that in a random selection of 100 colored candies, 26% of them are blue. The candy company…

A: Here we've to test that p= 28% = 0.28  So Hypothesis is, Ho: p=! 0.28 H1: p=0.28 Option (B) is…

Q: In a random sample of 80 male students at a college, 28 said they frequently send at least one text…

A:

Q: (d) If this hypothesis test is performed at the 1% level of significance, do the researchers reject…

A: There are two common error that exist in hypothesis test, they are type 1 and type 2 error. Where…

Q: A fellow student tells you the P-value is the probability that the null hypothesis is true, so when…

A: Meaning and usefulness ofp-value in hypothesis testing.

Q: When is a researcher at risk of making a type 2 error?   whenever H0 is rejected  whenever H1 is…

A: When is a researcher at risk of making a type 2 error?   A type II error that describes the error…

Q: A university claims that their employment rate directly after graduation is 80%. In a sample of 700…

A: Given that, x=609,n=700 The sample proportion is,

Q: Babies and younger boys are more likely to be diagnosed with peanut allergies. To test this claim a…

A: Given: Sample size for boys n1 =280 No. of boys diagnosed with peanut allergies, x1 =120 Sample size…

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.