A hair products company claims that a hair colouring treatment it produces lasts for an average of 45 days before fading. The company wants to check that its claim is valid. The hair of a random sample of 40 customers who had applied the treatment was monitored and the time that elapsed until the colouring faded was recorded. The mean time it took for the hair colouring to fade on these customers was 46.1 days with a standard deviation of 2.9 days. Do these results support the claim that the mean time the colouring lasts is 45 days? Use a 10 per cent level of significance.