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You are testing $H_0:渭=10$against $H_{伪}:渭鈮�10$based on an SRS of $15$$t$observations from a Normal population. What values of the statistic are statistically significant at the$伪=0.005$level?

(a) $t>3.326$

(b) $t>3.286$

(c) $t>2.977$

(d) $t<-3.326ort>3.326$

(c)$t<-3.286ort>3.286$

After checking that conditions are met, you perform a significance test of $H_0:渭=1$versus $H_{伪}:渭鈮�1$. You obtain a $P$value of $0.022$. Which of the following is true?

(a) A$95\%$confidence interval for $渭$will include the value $1$

(b) A $95\%$confidence interval for$渭$will include the value $0$.

(c) A$99\%$ confidence interval for$渭$will include the value $1$

(d) A $99\%$confidence interval for $渭$will include the value $0$

(e) None of these is necessarily true.

Does Friday the $13th$have an effect on people's behavior? Researchers collected data on the numbers of shoppers at a sample of $45$different grocery stores on Friday the $6th$and Friday the $13th$in the same month. The dotplot and computer output below summarize the data on the difference in the number of shoppers at each store on these two days (subtracting in the order $6th$minus $13th$).

Researchers would like to carry out a test of $H_0:{渭}_d=0$versus $H_{伪}:{渭}_d鈮�0$, where ${渭}_d$is the true mean difference in the number of grocery shoppers on these two days. Which of the following conditions for performing a paired $t$test is not met?

1. Random

II. Normal

III. Independent

(a) I only

(b) II only

(c) III only

d) I and II only

(e) I, II, and III

The most important condition for sound conclusions from statistical inference is that

(a) the data come from a well-designed random sample or randomized experiment

(b) the population distribution be exactly Normal.

(c) the data contain no outliers.

(d) the sample size be no more than $10\%$of the population size.

(c) the sample size be at least $30$.

Spinning for apples (6,3 or 7.3) In the "Ask Marilyn" column of Parade magzine, a reader posed this question: "Say that a slot machine has five wheels, and each wheel has five symbols: an apple, a grape, a peach, a pear, and a plum. I pull the lever five times. What are the chances that I'll get at least one apple?" Suppose that the wheels spin independently and that the fre symbols are equally likely to appear on each wheel in a given spin.

(a) Find the probability that the slot player gets at least one apple in one pull of the lever. Show your method clearly.

(b) Now answer the reader's question. Show your method clearly.

Refer to Exercise 1. In Simon鈥檚 SRS, 16 of the students were left-handed. A significance test yields a P-value of 0.2184.

(a) Interpret this result in context.

(b) Do the data provide convincing evidence against the null hypothesis? Explain.

A software company is trying to decide whether to produce an upgrade of one of its programs. Customers would have to pay $\backslash (100$for the upgrade. For the upgrade to be profitable, the company needs to sell it to more than $20\%$of their customers. You contact a random sample of $60$customers and find that 16 would be willing to pay $\backslash )100$for the upgrade.

(a) Do the sample data give good evidence that more than $20\%$of the company鈥檚 customers are willing to purchase the upgrade? Carry out an appropriate test at the $A=0.05$significance level.

(b) Which would be a more serious mistake in this setting鈥攁 Type I error or a Type II error? Justify your answer.

(c) Other than increasing the sample size, describe one way to increase the power of the test in (a).

According to the National Campaign to Prevent Teen and Unplanned Pregnancy, 20% of teens aged 13 to 19 say that they have electronically sent or posted sexually suggestive images of themselves. 'The counsellor at a large high school worries that the actual figure might be higher at her school. To find out, she gives an anonymous survey to a random sample of 250 of the school's 2800 students. All 250 respond and 63 admit to sending or posting sexual images. Carry out a significance test at the $伪=0.05$ significance level. What conclusion should the counsellor draw?

鈥淚 can鈥檛 get through my day without coffee鈥� is a common statement from many students. Assumed benefits include keeping students awake during lectures and making them more alert for exams and tests. Students in a statistics class designed an experiment to measure memory retention with and without drinking a cup of coffee one hour before a test. This experiment took place on two different days in the same week (Monday and Wednesday). Ten students were used. Each student received no coffee or one cup of coffee, one hour before the test on a particular day. The test consisted of a series of words flashed on a screen, after which the student had to write down as many of the words as possible. On the other day, each student received a different amount of coffee (none or one cup). (a) One of the researchers suggested that all the subjects in the experiment drink no coffee before Monday鈥檚 test and one cup of coffee before Wednesday鈥檚 test. Explain to the researcher why this is a bad idea and suggest a better method of deciding when each subject receives the two treatments.

(b) The data from the experiment are provided in the table below. Set up and carry out an appropriate test to determine whether there is convincing evidence that drinking coffee improves memory.

Refer to Exercise 2. For Yvonne's survey, 96 students in the sample said they rarely or never argue with friends. A significance test yields a P-value of 0.0291.

(a) Interpret this result in context.

(b) Do the data provide convincing evidence against the null hypothesis? Explain.