Suppose that a marketing researcher has been asked to determine if playing a new

Question

Suppose that a marketing researcher has been asked to determine if playing a new jingle on ice-cream trucks will increase unit sales from the current rate of 22 units/h. The researcher plans to conduct a one-sample ttest of the null hypothesis H0:=22 units/h against the alternative H1:>22 units/h, where is the mean number of units sold per hour. The researcher will collect sales data while playing the new jingle for one randomly chosen hour per day on one randomly chosen truck for a period of 14 days. The firm requires their results to be statistically significant at =0.01. The power of the test to reject the null hypothesis if the jingle will increase sales to 26 or more units/h is 0.85. What is the probability that the new jingle does not cause an increase in sales but the researcher recommends switching to it? Give your answer in decimal form, precise to two decimal places.

Explanation / Answer

Given that,
population mean(u)=22
sample mean, x =26
standard deviation, s =0.85
number (n)=14
null, Ho: =22
alternate, H1: >22
level of significance, = 0.01
from standard normal table,right tailed t /2 =2.65
since our test is right-tailed
reject Ho, if to > 2.65
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =26-22/(0.85/sqrt(14))
to =17.61
| to | =17.61
critical value
the value of |t | with n-1 = 13 d.f is 2.65
we got |to| =17.61 & | t | =2.65
make decision
hence value of | to | > | t | and here we reject Ho
p-value :right tail - Ha : ( p > 17.6078 ) = 0
hence value of p0.01 > 0,here we reject Ho
ANSWERS
---------------
null, Ho: =22
alternate, H1: >22
test statistic: 17.61
critical value: 2.65
decision: reject Ho
p-value: 0

we have enough evidence to support the claim

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