Perform a hypothesis test for the population mean. Assume that preliminary data

Question

Perform a hypothesis test for the population mean. Assume that preliminary data analyses indicate that it is reasonable to apply the z-test. Use the critical-value approach. 7. A car insurance company has determined that the mean annual car insurance cost for a family in the town of Watlington is $1716. A researcher wants to perform a hypothesis test to determine whether the mean insurance cost for a family in the town of Putford is higher than this. The mean insurance cost for a random sample of 32 families in Putford was $1761. At the 10% significance level, do the data provide sufficient evidence to conclude that the mean insurance cost for a family in Putford is higher than $1716, the mean cost for a family in Watlington.? Assume that the population standard deviation is $35.50.

Explanation / Answer

Here population standard deviation is given so we will use Z - test here.

H0 : = $ 1716

Ha : > $ 1716

Population standard deviation = $35.50

Number of families, sample size n = 32

Test Statistic :

Z = (xbar - )/ (/ sqrt(n))

Z = (1761 - 1716)/ (35.50/ sqrt (32))

Z = 45/ 6.2756

Z = 7.17

HEre for confidence level 0.10, critical value of z = 1.28

so here Z > Zcritical

so we can reject the null hypothesis and can conclude that mean insurance cost for a family in the town of putford is higher than this.

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