The sales team at SteelCraft Ltd claims that, on average, one of their agents sells $50K worth of supplies to each store that he/she visits per week. Their employer is wary of this claim and believes they may be overestimating.

To test the claim, the employer took a random sample of 6 stores that the representatives usually visit weekly and found the sales amounts to be $40K, $45K, $55K, $41.5K, $48.5K AND $46K.

At the 1% level of significance, can it be concluded that the sales team was incorrect in their estimation of earnings?

i.) Formulate the null and alternative two-tailed hypotheses.

ii.) Calculate the sample mean.

iii.) Calculate the sample standard deviation.

iv.) What are the critical values using a significance level of 1%?

v.) Calculate the test statistic.

vi.) Based on your answers to parts (iv) and (v) above provide a response to QAC whether the claim is correct.

vii.) What is the rationale for using two-tailed hypotheses?