1. True or False. Justify for full credit. (a) The standard deviation of a data

Question

1. True or False. Justify for full credit.

(a) The standard deviation of a data set cannot be negative.

(b) If P(A) = 0.4 , P(B) = 0.5, and A and B are disjoint, then P(A AND B) = 0.2.

(c) The mean is always equal to the median for a normal distribution.

(d) A 95% confidence interval is wider than a 98% confidence interval of the same parameter.

(e) In a two-tailed test, the value of the test statistic is 1.5. If we know the test statistic follows

a Student’s t-distribution with P(T < 1.5) = 0.98, then we fail to reject the null hypothesis at 0.05 level of significance .

2. Identify which of these types of sampling is used: cluster, convenience, simple random, systematic, or stratified. Justify for full credit.

(a) A STAT 200 professor wants to estimate the study hours of his students. He teaches two sections, and plans on randomly selecting 10 students from the first section and 15 students from the second section.

(b) A STAT 200 student is interested in the number of credit cards owned by college students. She surveyed all of her classmates to collect sample data.

(c) The quality control department of a semiconductor manufacturing company tests every 100th product from the assembly line.

(d) On the day of the last presidential election, UMUC News Club organized an exit poll in which specific polling stations were randomly selected and all voters were surveyed as they left those polling stations.

Explanation / Answer

1.

a) TRUE. beacuse by the definition of standard deviation - it is the positive sqaure root of the variance.

hence standard deviation can not be negative. it is always positive.

b) P[A]=0.4   P[B]=0.5   and A and B are disjoint then they can not occur together.

hence P[A and B]=0 and not equal to 0.2

hence the statement is false

c) TRUE. normal distribution is a symmetric distribution. hence the mean is always equal to median.

d) FALSE. because as the confidence increases the standard error of the statistic also increases.

hence the width of the confidence interval also increases.

so A 95% confidence interval is shorter than a 98% confidence interval of the same parameter.

e) since it is a two tailed test the p value is p=2*Min{P[T>1.5],P[T<1.5]}

now P[T<1.5]=0.98 so P[T>1.5]=1-P[T<1.5]=1-0.98=0.02

hence p value=2*Min{0.02,0.98}=2*0.02=0.04

level of significance=alpha=0.05

so p value<alpha

hence the NULL hypothesis is rejected.

hence the statement is false

2.

a) this is stratified sampling.

there are two sections which are the two strata and from each strata some students are randomly selected.

so the population is divided into strata and then a random sample is taken. hence stratified sampling

b) convenience sampling

She surveyed all of her classmates to collect sample data. hence the sample members are easy to reach for her since they are her classmates

hence the sampling falls under convenience sampling

c) systematic sampling.

here the test is done every 100th product from the assembly line.

hence a unit is selected at a particluar gap. the sample is determined after the first draw.

here like the sample will be -100th,200th,300th.......

d) cluster sampling

the whole population is divided into cluster which are the polling stations

then some clusters are randomly seleted and all the units which are the voters were surveyed.

hence a cluster sampling

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