Consider a random sample of32from3.12and7.1

size a population with hypothesized mean σ= .

Select the four parts for a one-sided, left-tailed hypothesis test concerning the population mean with α= 0.05 .

The null hypothesis is

H0:μ<3.12

H0:μ=3.12

H0:μ>3.12

The alternative hypothesis is

Ha:μ<3.12

Ha:μ>3.12

Ha:μ=3.12

The test statistic is

Z=xbar − μ0σ/n

Z=μ0−xbarσ/under root n

Z=xbar − μ0σ/√n

The rejection region is

Z⩾−1.6449

Z⩾1.6449

Z⩽−1.6449

Z⩽1.6449

What assumptions are made in order for the test in part (a) to be appropriate?

a) The sample size is large and the population standard deviation is known

b) The population is normal

Suppose the sample mean is xbar = 1.61 . Find the value of the test statistic.

(Give your answer to four decimal places.)

Z=

Select a conclusion about the population mean.

There is evidence to suggest the population mean is less than 3.12

There is evidence to suggest the population mean is different from than 3.12

There is no evidence to suggest the population mean is greater than 3.12

There is evidence to suggest the population mean is greater than 3.12

There is no evidence to suggest the population mean is less than 3.12

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