Question

Suppose that you wish to test a claim about a population mean. Which distribution should be used given that
the sample is a simple random sample, σ is not known, n = 40 and the population is normally distributed?
The z-distribution
a. The t-distribution
b. The Chi-Square Distribution
c. The F-distribution

1) A hypothesis in statistics is a claim or a statement about a
population parameter
legitimate inheritance
weather conditions
sample statistic

3) A market researcher selects 100 people as they left Square one Mall. What method is being used to select
the sample?

a. cluster sampling
b. stratified random sampling
c. Simple Random sampling
d. systematic sampling

1) Type I error is
the mistake of rejecting the null hypothesis when it is false.
the mistake of failing to reject the null hypothesis when it is false.
the mistake of rejecting the null hypothesis when it is true.
the mistake of failing to reject the null hypothesis when it is true.

5) Which of the following values could represent a correlation coefficient?
a. -1.045
b. 1.05

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c. 1.928
d. - 1
2) Which of the following would be an appropriate null hypothesis?
a. The mean of a population is equal to 100
b. The mean of a sample is equal to 100.
c. The mean of a population is greater than 100.
d. The mean of a sample is less than 100.

1) The width of a confidence interval estimate of the population mean decreases when the:
a. level of confidence increases.
b. sample size decreases.
c. value of the population standard deviation decreases.
d. all of these choices are true.

3) Assume n 1 = 382 and x 1 = 72, n 2 = 183 and x 2 = 69, calculate the pooled sample proportion .
0.125
0.175
0.225
0.250

The effectiveness of a headache medicine is tested by measuring the intensity of a headache in
patients before and after drug treatment. The data consists of before and after measurements for
each patient. Determine whether the samples are independent or dependent or neither.
Independent
Dependent
Neither
Not enough information

10) In a perfectly symmetric bell shaped "normal" distribution:
a. The mean equals the median.
b. The mean equals the mode.

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c. The median equals the mode.
d. All of these choices are true.

Answer 1

* Here, the researcher wish to test a claim about a population mean. Also, sigma is not known, n = 40 and the population under study is normally distributed, so t distribution should be used.

1): A hypothesis in statistics is a claim or a statement about a population parameter.

3): It is given that a market researcher selects 100 people as they left Square one Mall. The sampling technique used by researcher to select is simple random sampling as it give equal chance to every individual of being included in the sample. Here the researcher does not which people come out of the mall, so simple random sampling is the appropriate method to select sample. Hence option c) is correct.

1): Type I error is the mistake of rejecting the null hypothesis when it is true.

5): The range of the correlation coefficient values is – 1 to + 1. Therefore, the value could represent correlation coefficient – 1.

2): The null hypothesis statement considered as the hypothesis of no difference and the population parameter considered while the framing the hypothesis. Therefore, the appropriate null hypothesis would be the mean of a population is equal to 100. Hence option a) is correct.

1): The width of a confidence interval estimate of the population mean decreases when the level of confidence increases. Hence option a) is correct.

3): The given information is:

n1 = 382 and x1 = 72, n2 = 183 and x2 = 69

The pooled sample proportion can be calculated as:

Therefore, the pooled sample proportion is 0.250.

*In the study, effectiveness of a headache medicine is tested by measuring the intensity of a headache in patients before and after drug treatment. Here, the same patient or subject measured twice to see the effect of before and after drug treatment. Therefore, the samples considered to be dependent as the two measurements performed on same subject. Hence, the correct option is dependent events.

10): If the values of mean = median =mode, then only perfectly symmetric bell shaped can be achieved by the distribution of data set. It means that the statements in options a, b, and c are true. Therefore, the correct statement is All of these choices are true.

Hence, the option d) is correct.