Question

For this problem, please do all 5-Steps: 1. State Null, Alternate Hypothesis, Type of test, & Level of significance. 2. Check the conditions. 3. Compute the sample test statistic, draw a picture and find the P-value. 4. State the conclusion about the Null Hypothesis. 5. Interpret the conclusion. 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. 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.

Answer 1

Null hypothesis:  A car insurance company has determined that the mean annual car insurance cost for a family in the town of Watlington is $1716.

H0: mu_1=1716

Alternative hypothesis: The mean insurance cost for a family in the town of Putford is higher than that in town of Watlington

H1: mu_2>=1716

we will use t-test here since two towns are to be compared

level of significance is 10%

sample te test statistics=1716/(35.50/32^0.5)=273.442

p-value: observed level of significance

p-value=P(Z>273.442) where Z~N(0,1)

p-value<0.10 hence we rejec H0

and conclude that The mean insurance cost for a family in the town of Putford is higher than that in town of Watlington