Question

A researcher would like to determine whether a new tax on cigarettes has had any effect on people’s behavior. During the year before the tax was imposed, stores located in rest areas on the state thruway reported selling an average of µ = 410 packs per day with σ = 60. The distribution of daily sales was approximately normal. For a sample of n = 9 days following the new tax, the researcher found an average of M = 386 packs per day for the same stores. a. Is the sample mean sufficient to conclude that there was a significant change in cigarette purchases after the new tax. Use a two-tailed test with α = .05.

Answer 1

We conclude that there was no significant change in cigarette purchases after the new tax.

Explanation:

We are given that during the year before the tax was imposed, stores located in rest areas on the state thruway reported selling an average of µ = 410 packs per day with σ = 60.

For a sample of n = 9 days following the new tax, the researcher found an average of M = 386 packs per day for the same stores.

Let
`\mu` = mean cigarette purchases after the new tax.

SO, Null Hypothesis,
`H_0` :
`\mu` = 410 packs/day {means that there was no significant change in cigarette purchases after the new tax}

Alternate Hypothesis,
`H_A` :
`\mu`
`\\eq` 410 packs/day {means that there was a significant change in cigarette purchases after the new tax}

The test statistics that would be used here One-sample z-test statistics as we know about population standard deviation;

T.S. =
`(M-\mu)/((\sigma)/(√(n) ) )` ~ N(0,1)

where, M = sample mean selling of packs/day = 386 packs/day

σ = population standard deviation = 60

n = sample of days = 9

So, the test statistics =
`(386-410)/((60)/(√(9) ) )`

= -1.20

The value of z test statistics is -1.20.

Now, at 5% significance level the z table gives critical values of -1.645 and 1.645 for two-tailed test.

Since our test statistic lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that there was no significant change in cigarette purchases after the new tax.